The technically correct thing to do would be to educate on precision, perhaps even display it, such that people know that 12:00 means a time between 11:59 and 12:01, not 12:00.000.
And yes, 5-to-15-to-an-hour is something that varies, depending on the length of your trip. 5 is appropriate when you're in your office and you need to get to the conference room, 15 if you're driving from your nearby home, an hour if you're flying in, or if you have to drive 200 miles or so -- particularly if it's a trip you don't regularly take!
For meetings, I actually give myself 16 "precise" minutes -- one minute less than 15, with 4-minute-30-second snoozes, so I can have both adequate warning, and regular pokes, to make sure I can do something on time.
How long between 12:01:00.0 and 12:00 (as read on a clock)? Between 0 and 60 seconds.
How long between 11:59:00.0 and 12:00 (as read on a clock)? Between 60 and 120 seconds.