There are a lot of blanket statements in this thread, that even if they are accurate in the state you're familiar with, need an asterisk next to them because these laws tend to vary from state to state.
I have heard stories here in Indiana where there are people who year after year hunt property lines, make bad shots on animals, then want to stomp all over their neighbors ground for the rest of opening weekend looking for their deer, effectively ruining the other person's chances. I can understand this happening once or twice, but if it becomes a pattern year after year then I can understand a landowner eventually denying access. This is, of course, a different scenario than having an animal down within sight of the property line.
I am fortunate that in each of my private property spots we have good relationships with the neighboring landowners. If I need to grab a deer on their side no problem, they need one on ours no problem. But when I hunt public, and don't usually know the adjacent private property owner, I try to give a fairly wide berth to the boundary to allow for a 100-yard death sprint.
And I've never had to do it either, but like some others have said, if the deer is within sight of the line I'm going to grab it, even if it does mean risking a ticket.