You're right that Putnam's point is stronger than what I initially made it out to be, but I think my broader point still holds.

I was trying to avoid this complication but with two-dimensional semantics, we can disambiguate further and distinguish between the C-intension and the A-intension (again see the Stanford Encyclopedia of Philosophy article for explanation). What I should have said is that while it makes sense to be externalist about extensions and C-intensions, we can still be internalist about A-intensions.