I really doubt it works that way. The law, at least in many U.S. states (as I posted above), requires you to notify the other party if you're recording the call. I doubt it really matters what the other party is doing. Each person who is recording must give notification that they're doing so.

You're logic is like saying, if I take my car to a mechanic and sign the estimate for repairs, which is also a waiver giving the mechanic permission to do the repairs, that therefore means that I also have the right to work on the mechanic's car.

Granting one party permission for a specific activity, doesn't just automatically grant all parties permission for a specific activity. I'd say, if you haven't made it explicit that you're recording the call, then you're breaking the law.

The point of the law, after all, is that people are supposed to know the call is being recorded by a specific party. The fact that I tell you that I'm recording a call, in no way gives me knowledge about whether or not you're recording the call.