Exactly.
You are renting for a DAY, not for a PARK.
Each day's rental pass is stamped with the date it is used. When you return your stroller, you can get a ONE DISNEY DOLLAR refund, but in order to do that you have to hand in that day's rental pass. If you think you even MIGHT be hopping later that day, or returning to the same park for that matter, then DON'T hand in the rental pass/get the refund. If you're not seeking the refund at that time and you're in the mood to be VERY rude, you don't even need to return the stroller, you could just leave it anywhere on your way out of the park.
If you end up NOT hopping that day, you can get the refund at any later time.
When I went last year and got a multi-day rental, they stapled my strip of rental passes to my receipt. Well, when I went to actually pick up my first stroller, the CM date-stamped the rental pass at the top of the strip, the one with the staple in it. If I detached that from the rest, I would have then had 2 pieces of paper to lose (receipt and strip of remaining rental passes). So, to make a longer story not quite so long, I never turned in any used rental passes for a refund until the last day I was in a park, and I got a whopping $6 in Disney Dollars back at that time.