The USA is home to some of the best flying and training in the world, but also some of the worst. The problem with cheap schools in the USA is that they usually aren't cheap. There are a lot of shady operators out there.
Ari-Ben is the perfect example. The $34,995 in the example posted above has small print: Add $6000 for the FAA PPL. There's also thousands of dollars of additional costs, about another $10,000, including a random 'Admin fee', and $1500 of 'Fuel Surcharge'. They don't even include any books in the package price. Also, many of the hours flown at Ari Ben are as 'Safety Pilot', not valid under JAA. The quality of training also suffers in these big schools, where one batch of student's goes on to teach the next.
A better choice is to look for a small FBO offering 141 programs, who also have the ability to issue visas. They will be significantly cheaper than the academy style schools, and generally have more experienced instructors, a more varied fleet of airplanes, and better availability of airplanes and instructors, meaning you'll save a lot of time.