That's an old urban legend that goes back even a generation before in firearms.
It's just not so. :)
Hardly, the 5.56X45 is (45 mm long) longer than the 5.45X39 (39mm long) The 5.45 has a fatter case, being derived from the 7.62x39, and only requiring a different magazine and barrel (plus maybe some tuning of the gas system and springs) to be changed (in design) when going from the -47 series to the -74 series. The bolt face and extractor didn't need to be changed, since the rear end of the two catridges (7.62 and 5.45) are the same size and shape.
A 5.56 wouldn't fill the hole in the 5.45 chamber, side to side that is, but it would jam up (or slam fire) because of the excess length of the loaded round.
This is an old myth that's been around for ages.