It essentially is one of the unwritten rules that holding a weapon in one hand (or both hands) precludes you from using any natural weapons such as claws or an arm-based slam attack with the same limb during the same full attack action.

This is never explicitly stated, but it bears out in every monster stat block that exists for monsters which have both manufactured weapons and a potentially conflicting natural attack form.

Unarmed strikes are one good example that gets around this limitation, since they can be used with various parts of the body. Some slam attacks can also be considered more like full body checks rather than "special punches", and could also get around the limitation. (I think many of the monsters that get two slam attacks are doing so because they're using their arms, and it says this somewhere in the rules which I forget exactly.)

I would bet that tentacles could also be blocked in a similar way if you used one to wield an actual weapon, like if an awakened octopus decided to swing eight swords around or something, it would have to use multi-weapon fighting rules and couldn't use its tentacles to attack normally. Or if you hold a sword in your mouth like some kind of anime protagonist, you can't also bite someone on the same turn.