Eles precisam de nós.
The need us.
Eles exigem de nós.
They require us.
There is a difference in meaning.
I agree with you completely
Why the "de"? Would it mean something different without it?
It says in the theory part that "precisa" and "gosta" always require "de". It's just the way they use those verbs in portuguese.
Would sound weird.
Why "they require us" is not valid?
I think 'precisar' might be linked to 'precious'. In that case this sentence woudn't mean 'we are required' but more like 'we are invaluable'.
The only meaning I see for this sentence is "we are required".
precisar is the verb need (they needs us)