I am having this problem now as well.
I have another user who is an administrator, and whose permissions mirror mine. I have checked their user security, company membership, and workspace membership(s).
I have read the Help wiki and searched the forums exhaustively.
For some reason, this person who is an administrator cannot assign a task to a person in another client company... We have one owner company (which none of us are employees of) and then we all are members of client companies below that one.
I am an administrator and I can assign a task to anyone. He, however, cannot.
Any ideas?