Unfortunately your second sentence is not correct; patents do this overclaiming game all the time.

(not a lawyer, co-inventor on three patents so I've been through this, unfortunately as I didn't want to participate in that system, consult a lawyer before doing anything rash).

The claim matters, not their detailed description. The most harmful patents work that way: describe in detail a specific implementation, but write the claims to cover every alternative implementation you can think of.