You are misreading it mate.
It is about "initial" training in the US.
It does not follow logically that the initial training in the US will be a PPL.
So if I have a, say a Barbadian PPL, I can go to the US for my CPL (note Barbados does not issue CPL's) - that is initial training in the US - though not my initial flight training - in that circumstance I need the TSA check.
It's about getting you in the system.
In the same circumstance where the PPL was obtained in the US - you do not get TSA'd again as you are already in the system.
You seem very happy to deconstruct my comments except the killer one - I have done it several times and I am very upfront about why I am in the US and what I will be doing - the flight school make sure you are legit too as they get it in the neck if they train anyone who is not.