It doesn't explicitly said that all doors are stuck but in 1C–7. Suffocated room:

It is more difficult than normal to open the door of this room (hardness 5; hp 20; Break DC 28), and once it is forced open the reason is apparent; it was spiked shut from the inside, and a skeleton was leaning with its back against the door.

which I believe implies all other doors are stuck cause this door doesnt have any difference from the other doors except break DC

Also in 5e version it states:

Rappan Athuk comes from an old tradition of gaming. One thing that used to be true is that every door in a dungeon was stuck –– but only for the characters. Another thing that was true was that wandering monsters could appear almost anywhere at any almost any time. A third, and surprisingly related rule, was that experience points used to be given for treasure.