Is your university asking you to do this? Are they actually telling you to go round up a bunch of student letters? If so, go for it. (Actually do whatever you want, I'm just telling you a true story about a guy who really screwed himself over by doing this.) The universities I am familiar with (which is only a handful) prefer to handle contact with students using a third party (a faculty committee member, a department chair, a university staff member) instead of having a faculty member recruit positive student letters under mysterious circumstances.
There is nothing at all wrong with asking a few selected students for a letter. How else would you get them? Just don't ask anyone currently taking a class from you.
How did the guy in your situation bribe/strong-arm them? How did he get caught?
Was he denied *because* of this, or would he probably have been denied anyway?
I don't think there's anything wrong with asking per se, but I would want to be careful with it looking like a quid pro quo.