Checked in recently at a CY and asked if I could get an upgrade. Was
told by FDC nothing was available. Was given a general room. As soon
as I got in room went on internet at Marriott reservations and found that
there were larger rooms and suites showing availability. This was about
4 PM. Checked several more times and still availability as late as 11:30 PM
that night. Next morning asked FDC about this and he said that Marriott
overbooks rooms and his room count will show negative (?) and that he
cannot upgrade rooms at checkin when he is holding those for confirmed
reservations. He says that Marriott reservation system allows them to
overbook because a lot of the time people don't show up.

I called Marriott reservations three different times and spoke to three
different people and they all say that Marriott does not overbook.

What has been the experience with others in this type of situation?

Yes they do overbook (constantly, like airlines, its how they make some extra cash) - though they are generous if you are overbooked. This is how the platinum over-ride works for example (i.e. the guaranteed availability with 48hours notice). Marriott.com always seems to offer more rooms than the hotel's front desk is ever willing to let you book as well. So there could certainly be scenarios where marriott.com is saying "I can sell/overbook another 2 rooms" and the FDC is looking and seeing "I have 40 rooms available and 43 reservations" - the point is that the marriott.com is a complex booking system which makes 'bets' on the number of expected cancellations and no-shows, whereas the front desk just don't want to have to walk a guest.

Don't forget that an upgrade to a suite is never a published benefit or a right, and so those rooms weren't really available for upgrade (of course some properties do upgrade to suites etc). Whether this is or isn't the case in your particular scenario is of course a different question - personally if I was checking for an upgrade at 11.30pm I might wonder about whether I should have just paid for the better room - its one of those things for me, I'm sure that it happens all the time!

Edit in my own view I think the fdc probably fibbed as most room bookings are likely to be for basic rooms so the overbooking wouldn't really come into it, but it could be the case, its unfair to always distrust people!

If I want a suite I pay for it.....

It's a CY, what do you expect?

Reservation does not have access to inventory counts, they only tell the computer what your looking for and the computer comes back yes it's available or no it isn't but here's other options.....all hotel's regardless of flag overbook as appropriate