Hi,
and welcome to the forum. I'd suggest to post any future questions regarding flying in the US in the "North America" section of the forum.
But a student with a tourist visa is able to receive training in a part 61 flight school?
NO! This would be absolutely illegal, no Part 61 school would do this! That's one of the reasons why the TSA (Transportation Security Administration - Department of Homeland Security) was established, in the aftermath of 9/11. I believe that just even showing up at a school and making this kind of inquiry could rise serious suspicion and they might inform law enforcement. All flight school employees must take regular tests and are trained to report any suspicious persons and events.
To my knowledge in order to train international students a flight school must be Part 141 certified. Reason being, the school must have TSA approval (see link below) in order to offer a visa program.
https://www.flightschoolcandidates.g...e=c§ion=WN - see FAQs tag
Check out the following link, it basically confirms my statement.
http://www.pprune.org/professional-p...ml#post7638560