As others point out, Disney will let you use a FP later the same day. The person that had a wallet full of passports was breaking the rules, and in general in my view they DO check the date frequently. But, as far as using them late on the same day, we do this a lot, and have never been stopped before.
Especially at MK - I typically go and grab a FP every time I am eligible. Admittedly we go at a slow time of year, but for example:
When park opens, we get FP for Peter Pan:
Return time 9:50 - 10:50 next eligible FP: 9:50
@ 9:50 we get FP for Jungle Cruise
Return time 10:30 - 11:30, next eligible FP: 10:30
@ 10:30, we get FP for BTMRR
Return time 11:15 - 12:15 PM, next eligble FP: 11:15 AM
@ 11:30 PM, we're over in tomorrowland - get a FP for Buzz Lightyear
Return time 12:10 - 1:10 PM, next eligible FP: 12:10 PM
@12:10 PM still in tomorrowland - get a FP for Space Mountain
Return time 3:30 PM - 4:30 PM, next eligible FP: 2:20 PM (2 hrs after I got that one, since the return time is > 2 hours out.)
So, now I have 5 sets of FP (Peter Pan, Jungle Cruise, BTMRR, Buzz Lightyear, Space Mountain), which now that it is mid-day and the lines are all long, we go back through the park and use them. Meanwhile, we can still gather MORE FP as we go for using later. We usually don't stay in the park real late, so I don't think I've ever gotten more than about 8 sets of FP. At a busier time of year, the return times might be a lot more spread out. An example of this is at DHS.
Got FP right at Rope Drop before riding TSM Standby - return time 9:50 AM -10:50 AM.
Come back to TSM at 9:50 AM for another set, this time return time is 2:30 PM - 3:30 PM. Next eligible is 11:50 AM (two hours later).
At 11:50 AM, the TSM FP were all gone for the day. But we did get to ride it 3 times with very little wait.
Of course, the flip side to Disney allowing this is the FP return lines are much longer late in the day. (I don't care what Robo says, it DOES affect the FP crowds Disney allowing this.)
Does that all make sense?
Added: I should point out that I am the "FP runner"...I take everyone's tickets and go and get the FP - we usually try to pick up FP for rides that are not too far away from us, but in the past I've run across the park and back to do this. Usually while the others are taking a potty break or doing a little shopping. (You should NEVER do a FP run while your family is "saving" a spot in another line for you. that is extremely rude.) But to the PP that said you don't really "gather" them, I think getting a set every 30-45 minutes and running around the park to get them follows the very definition of "gathering".