Whatever they say, they CAN NOT provide you flight training for FAA PPL without a student visa. This is NOT allowed on the Visa Waiver Program.
Let me say this again:
It is illegal, and you will get in trouble.
They can be provider for TSA purposes, but to enter the country for flight training, you need a visa. You can not enter the US without a visa if you intend to train for an initial license or rating, simple as.
Who gave you that advice, name and shame. They should be reported to INS and FAA immediately.