The rule says "in a natural break in programming".
Stations have been putting the ID at the end of the hour's last stopset for decades. The FCC has not objected.
I am not suggesting that stations not identify per the rules. I am just observing that stations like to put the ID where it does not interrupt a music sweep, and that is legal.
Back when the ID had to be within +/- 2 minutes of the hour, I once got an FCC notice because the ID was 3 minutes off; it was summer and WWV had no signal into Puerto Rico most days, so getting the clocks set was sometimes hard. We explained this, and put up a better antenna and one of those $500 ESE radio clocks (about $3000 in today's dollars) and generally were OK except when there was no signal at all.
Many colleagues got similar notices, some as many as 5 or 6 times in a year for the same reason. The FCC never fined anyone. Fines are for willful and repeated violations of this type. When WWV was not available, there was always an excuse.
Now, the rule is much more flexible and, save technical errors, stations run IDs at a "natural break".
Many, if not most, FCC notices of violation have no fines. They simply demand corrective action and a response.