tenant reported that occasionally he hears the toilet flushes itself.

it does not follow a pattern like every hour or every 2 hours, he said it may not happen at all for 3 hours and when it happens and after that it may happen again after 30 minutes but after that may not happen for an entire day.

I went to investigate and could not reproduce.

first of all I could not think of a situation that a toilet can flush itself (meaning the flapper raises by itself), so I think by "flushes itself" I think he meant to say the fill valve activates and gives off this hissing sound as it refills and that's what he means by "flush". If that is the case, it could be a slow flush valve leak from say a deformed flapper and as water leaks out the water level in the tank drops till a certain level to activate the fill valve. BUT the problem is if the flapper is leaking it should not be a random thing it should be refilling every so often right? What am I missing?

The flapper valve rests on the outlet at different angles on different flushes. This has happened to me. If I set it at correctly (by hand) it doesn't leak. Make sure its chain isn't interfering. Here's a doc I wrote:

A study by the East Bay Municipal Utility District (EBMUD)
(Residential Indoor Water Conservation Study: evaluation of high
efficiency indoor plumbing fixture retrofits in single-family homes in
the East Bay Utility District Service Area
[www.cuwcc.org])
reported that leakage was the number one water user in the surveyed
households ('After the retrofit, leakage (17.1 percent), which had
previously been the largest component of indoor use dropped below
toilets into fourth place.') The number one cause of leakage was
defective toilet flappers: 'A reduction in leakage resulted in a
surprisingly large savings of 16.8 gcd. The leakage savings were
almost certainly the result of the toilet retrofit. Toilet leaks,
primarily flapper leaks, are the single largest contributor to
household leakage. In this study, replacing old toilets through the
retrofit eliminated almost all of these toilet leaks and resulted in
substantial savings.'

EBMUD implicated the water utility's switch from chlorine to
chloramine: 'One possible explanation for the high leak rate that was
found in some of the study participants' homes could be traced to the
District's change in its water treatment process. EBMUD converted from
treating water with chlorine to chloramines (chlorine and ammonia) in
1998. An August 1993 AWWA Journal article reported study results
showing that chloramines have a more deleterious effect on elastomers
(products widely used in plumbing distribution, especially for toilet
flapper valves) than does free chlorine. When a utility converts from
chlorine to chloramine, this negative effect on the elastomers tends
to increase incidents of leaks in the home and in the distribution
system. Leakage accounted for 30.3 percent of indoor per capita use
prior to the retrofit and 17.1 percent after the retrofit.'

The Canada Mortgage and Housing Corporation in 'Dual-flush Toilet
Project'
[www.cuwcc.org])
reported: 'Savings related to reduced toilet leakage equate to 176
litres per suite per day' (as opposed to only 124 litres per suite per
day saved because of the efficiency of the toilet), with the note
'Note that it is likely that this reduction in leakage would have been
achieved by installing any non-leaking toilet, or perhaps even by
replacing the existing toilet flappers (flush valves)'.

The Seattle Home Water Conservation Study 'The Impacts of High
Efficiency Plumbing Fixture Retrofits in Single-Family Homes'
(http://www.cuwcc.org/toilet_fixtures/Seattle_Final_Report_Dec-2000.pdf)
reported, 'A reduction in leakage resulted in savings of 4.3 gpcd. The
leakage savings were almost certainly the result of the toilet
retrofit. Toilet leaks, primarily flapper leaks, are the single
largest contributor to household leakage. In this study, replacing old
toilets through the retrofit eliminated almost all of these toilet
leaks and resulted in substantial savings.'

The Metropolitan Water District of Southern California (MWDSC) in
'Toilet Flapper Materials Integrity Tests'
(http://www.cuwcc.org/toilet_fixtures/Toilet_Flappers_Integrity_Tests_2000.pdf)
found that 'some in-tank bowl cleaners would cause severe warping,
swelling, blistering, and cracking of the typical flapper, leading to
a leaking flush valve.'

MWDSC, in its monumental 'After-Market Toilet Flappers: A study of
compatibility and flush volumes'
(http://www.cuwcc.org/toilet_fixtures/Toilet_Flappers_Integrity_Tests_2000.pdf),
observed: 'A typical tank-type porcelain toilet is believed to possess
a useful life of at least 20 years. However the flush valve closure
device (usually a flapper) within the tank of these new ULF toilets
may fail within 5 years, due either to normal "wear and tear" or to
other factors introduced by the consumer. Failure leads to water
leaks that could, unless corrected, substantially erode the water
savings anticipated over the 20-year life.' and studied 50
after-market flappers for ultra-low flush toilets. They found that
many don't fit properly and others are hard to adjust, undermining
their water-saving. In this paper they tested and rated 50 flappers.

The National Association of Home Builders' Research Center in 'Water
Closet Performance Testing Report No.: P01-1660902'
(http://www.cuwcc.org/toilet_fixtures/Seattle_Final_Report_Dec-2000.pdf),
prepared for Seattle Public Utilities and East Bay Municipal Utility
District found, 'Because flapper valves typically require replacement
several times during the useful life of a toilet fixture and the
likelihood that the consumer will install a generic replacement
flapper, water efficiency of many of the tested models could
significantly degrade over time.' and recommended, 'The plumbing
industry in coöperation with the water utility industry, should
develop a parts identification and distribution system for flush valve
flappers that will assure that the consumer will purchase the
appropriate replacement flapper to maintain the 1.6 gpf that the
fixture was designed for.'

The Los Angeles Department of Water and Power (LADWP) requires
flappers to be tested by a third party; it publishes a list of
approved flappers
(http://www.cuwcc.org/toilet_fixtures/Seattle_Final_Report_Dec-2000.pdf)

You may have picked up my point by now: studies have found that:

1. replacing old toilets with more-efficient toilets saved more water
because so doing eliminated leaks in toilet flapper valves rather than
because of the greater efficiency of the new toilet;

2. generic flapper valves often don't fit (or can't be adjusted to
fit) new ULF toilets;

3. new chemicals used by utilities in water treatment corrode
old-style flappers more than chlorine;

4. in-tank cleansers many consumers put in their toilet tanks corrode
old-style flapper valves quickly;

5. consumers often don't make the effort to purchase appropriate
replacement flappers or adjust them properly.

Sum, I agree the tenant is hearing the fill valve run intermittently and calling that a "flush". It sounds like the flush valve flapper is failing. In its early stages of deterioration the flapper seals sometimes, depending on how it lands when it closes. If it happens to seal, the toilet may not run for days or even until the next flush. If it lands heavier on a worn edge, it will leak and cause the fill valve to run more frequently.

This is the early warning on the flapper, I would put it on the list to fix and see if that fixes the problem, it's only going to get worse.