A bit confused by your anecdote.
They did not lie.
A Staffordshire Bull Terrier IS a pit-bull Terrier, full and clear.
A PBT is a TYPE, not a breed only. It covers several breeds including some very large ones. The deception is those who KNOW damn well PBT covers a whole range, but try to tell you only those with the “pit-bull Terrier” words in the name are that. Trust me, an “American bulldog” is fully bully/PBT. The Operative is they were bred using bulldogs and PBTs of some fighting type.
In fact, some dogs fall under the fighting type category, but the fight has been bred out of them. Thus, I generally trust Bull Terriers, Bulldogs and Boston Terriers.
Anyway, just have to go over that. Your people were not lying. You just need to know a Staff is a PBT.
You are correct, they did not lie. But had they said, “Here is a Staffordshire Terrier commonly know as a pit bull.”, we would have saved a trip to the shelter and ended up with the Newfoundland on the first trip.