There are 2 different ambiguities there: 1. Ambiguous may, which could refer to permission or to possibility 2. Doesn't specify which party is permitted to do

There are 2 different ambiguities there: 1. Ambiguous may, which could refer to permission or to possibility 2. Doesn't specify which party is permitted to do the recording/might be doing the recording Makes me wonder why that phraseology is so widespread. Why not use We might record this call?