A visa is not required (and indeed cannot be issued) for a course involving less than 18 hours of training per week,
While you are probably right, and I agree about the "18 hours" bit, it would not be wise to try this on the usual heavily armed and aggressive U.S. Immigration Service official, by telling him/her that you are going to do flight training and you don't have a Visa for it because of such and such bit of US Law.
There is no doubt that a lot of FAA training does not need TSA, e.g. the Commercial license, and there are clear references for this from the DHS, US AOPA, etc.
But none of this will wash in practice. Somebody going to the USA either needs TSA+Visa, or has to go there on a "holiday" and pop over to some small informal school whose owner has sufficient intelligence to read these rules and realise that if he was subjected to a TSA check all would be OK... the big schools tend to adopt a hand washing attitude and they want ALL the paperwork.