Well, you're entitled to your own opinion, just not your own facts. The fact is that we know the forces required to pedal a bike, road or mountain, and the fact is they are well below what a functional person is able to generate. If someone is able to walk up two or three steps, they are able to generate all the force necessary to produce the maximum power we see. Now, I notice you put strength in quotes. If you're doing that to indicate you define strength in some unique way known only to you, it's quite possible you're right; but I have no idea what you're talking about. I don't put it in quotes and use it in the way physiologists have always defined it; as the maximum force or tension a muscle or muscle group can generate. From that, it can easily be seen that if someone can turn the pedals over once, strength is not a limiter. For example, the only place where it mat be a limiting factor is for standing starts on the track where the rider can't generate enough force to get the bike moving.

Finally, the fact that your strength training improves your performance does not prove that was due to increased strength. Post hoc ergo propter hoc. Another fact is we know is that all training interventions have many cross-over benefits, so even pure strength training (and we don't know if that is what you were doing) can improve aerobic performance.