No. They aren’t saying that “age” sounds like ‘h’. They’re just close enough that any acoustic imperfections in the room (or the body of either person) could cause one to be misheard as the other.

A-g (age)

A-ch (H)

Ache doesn’t sound like H, it sounds like ake. When we say age it sounds like eidg, which might sound somewhat similar to aitch.