Prior to 2001, flight school regulation has been minimized to the technical level. Meaning to say, the government agencies that may have an interest on them are those that are primarily related to aviation regulation. Since September 11, 2001 when two airplanes crashed on the Twin Towers of the World Trade Center in a terrorist attack, entering a flight school now would entail passing through a tougher screening process.
Any aspiring pilot must pass a given set of requirements for the appropriate authorities to determine whether you are a security threat or not. In fact the TSA has a separate category for non US citizens (or aliens) in taking up flying lessons. Apparently, these regulations were enforced in 2004 as a precautionary security measure so that the 911 terrorist attacks would not happen again. It was stated that the terrorists that flew the passenger airlines to the the World Trade Center buildings were trained on American soil.
If you are an alien who is seeking to be a pilot, then simply complete the necessary documents and tests prior to getting that license. Sure, it's an added requirement but you'd have to understand that there have been many instances when airplanes have been used literally as weapons of terrorism. Ensuring that you submit the proper requirements and get the proper training could spell a big difference for the safety of your future passengers.
One can only understand these new regulations in the context of these terrorist attacks. They're not meant to discourage you from ever achieving your dreams of flying, but rather to protect people both on the ground and in the air.