They probably could've done it regardless of what they're profession might have been. They were intuitive, persevering, and clever. Which is not to say that knowing how to build bikes didn't help them. The two things that I find most amazing are that they actually built the engine, and that they designed and built the first wind tunnel and did testing to find the ideal shape of the wing.

Could only bike makers have done it? Well, they were inspired by the work of Otto Lilienthal, who had a fair amount of success with gliders, but I believe no experience with bikes. On the other hand, he died in a glider crash.