It has nothing to do whatsoever with the FCC and everything to do with revenue at local stations.
The big money revenue-getter program at most stations is the late, 11 PM news. For years, in the '50's and '60's and beyond, the news only ran to 11:30, starting and ending on the half-hour like most shows do. In fact, some stations only managed to eek out a 15 minute newscast - and THE TONIGHT SHOW and NBC actually provided an extra 15 minutes of lite-chat prior to the 11:30 official start time.
When the local stations figured out that they made their most money from that half-hour, they lobbied and got their networks to push the 11:30 shows back by 5 minutes. Why? So they could sell five minutes more advertising WITHIN their 11 PM newscasts.
A similar phenomenon exists with popular network shows. Check when LOST or CSI: airs. You'll find that they start on time, but end a few minutes into the next hour. That's so that the networks can sell more minutes WITHIN those shows. And they'll actually run fewer commercials in the shows that follow.
For the 10:00 hour, the networks sometimes start a popular show a minute or two early. Back in its final few seasons, E.R. used to start at 9:58 PM.