Don't they simplify it? You're on the call. If you consent to recording, you've given your single-party consent. You don't need to tell the company you're calling you're recording.
This is possibly worse than staying silent, given you're betraying bad intent.
IANAL but AFAIK the "this call is recorded ..." warning that they automatically play gives license for both sides to record, even in a 2 party consent state.
They were trying to screw me, and the state insurance commissioner finally had to step in and put them in their place. The person who caused the accident had the same carrier I did, and since they knew they were on the hook for the charges either way, they made no effort at all to adjudicate fault. They wanted to split it 50-50, and I wasn't having it.
Funnily, the phrasing "may be recorded" is not interpreted by the corporations as "the customer may be recording as well" and in many cases their default policy is to not talk to you if you've declared you're recording. Single-party consent jurisdictions make it even more muddy.