IIRC the risk was never because of overpressure, it was because the ATGMs use a solid propellant which when combined with the generally rough handling of the autoloader and possible high internal barrel heat could lead to some explosive consequences. This is a vague memory of mine, so if this is just some misremembered fuddlore kicking around in my head, I wouldn't be surprised.
For context, the T-80 autoloader:
Vs how the BMP-3 autoloader loads a missile:
BMP-3s autoloader seems a lot more conducive to safely loading the more highly-explosive and heat+shock sensitive solid-propellant missiles.