The "realistic" cutoff is one of 99/100/101. I read it a while ago, but I can't quite remember. I've seen a record of 101 while playing, I can't remember anything less.
If I were to write a program to solve these puzzles, I'd expect it to run in a couple seconds, tops. I did write a program to solve sudokus once. Puzzles that I could manually solve in 200-300 seconds took less than a second in processing time. I don't think I implemented the screen-scraping/parsing, I just manually input a couple puzzles and ran the thing to see how it did. Now, on that site, I am sure people were automating because it showed solve times on a bell curve, and there were always some under 5 seconds.
The "realistic" limits here are too high, but I'm betting the fast solvers see "new record" more often than we really achieve it, not that it gets saved as such. I solve the 4x4s in under 100 seconds about half the time now, with my best times being in the 60s. I'm usually closer to 200 seconds for the 5x5s, but I've done a few of them in under 100 seconds as well. Of course, whatever the limit that is set, it is easy for a computer program to put a "delay until time is just over this boundary" statement in, if the goal is to set records.