You may be right about congress, but in this case we're not talking about laws but regulations. Regulations are enacted by agencies, and Congress passes appropriate laws so the agencies regulations have some teeth.
In the present case: the aviation regulations -- the FARs -- are all about exactly how things are done. Try reading an airline's Ops Spec sometime -- it spells out exactly what is to be done and how, for all operations conducted by the airline. The FAA specs on navigational beacons lay out everything about the system, not just what but how. This ensures that all users of the ATC system have the same view of reality.
So of course ATC (not "tower") cares about exactly how the information is sent from an aircraft to the system. ATC does in general care about what kind of nav system you're getting your info from, since the different systems have different error characteristics. (Also, this is an automated system, we're not talking about pilot reports.) All the information required for a company to implement the components of the system -- like the airborne transmitter -- is fully specified.
Radar doesn't require an active participant on the other end.
Not true. You're thinking of what's called "primary" radar, where the target reflects the transmitter's signal. The problem with primary radar is that range falls off as the inverse fourth power of signal strength -- inverse-square loss on the way to the target and another inverse-square from the target. That's why most ATC radar is "secondary" -- there is a specialized transmitter on the airplane (called a transponder) that the radar system interrogates, and the aircraft replies with its ID, altitude, and a couple of other things. Since it's an active system, it's ordinary inverse-square falloff, and it provides more information. (If you look carefully at airport radar installations, you'll notice that there are two antennas spinning together, one above the other. The "secondary" antenna is usually on top and flat; the primary is on the bottom and is usually paraboloid.
Today, in the US, primary radar is almost never used; most controllers configure their screens to not show "primary only" targets.