So basically you're saying that it is possible for us to play a victim of the illegal Esper program but you are essentially all but forbidding it by telling absolutely nothing about it Why even bring it up as a source for our character's powers?
A couple of people have already managed to incorporate the illegal Esper program into their character's backstories even with very little information. Very little information is known about them to the general public, other then they are experimenting with superpowers and superhumans and a lot of their 'subjects' are not participating willingly. That should be more than enough to go on.