Fun times, try telling those same corporations that you're recording the call. I've yet to have any proceed other than (politely, but promptly) disconnecting the call.
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?
Gonna be a fun call with PayPal tomorrow!)
If this took place in a two-party consent state then your consent alone is not enough, you'd also need the caller's consent which my company doesn't have. If you were to record the call without letting the employee know beforehand, that recording would be illegal.