No, copyleft does not fundamentally depends on strong copyright law. That is just an implementation detail. It would work just as well--better, actually--if it was enshrined in actual law. In fact, I understand this is what the movement actually wants; unfortunately,a law like this is unlikely to get through the legislative process. Happily, we can use some "legal judo" to turn copyright onto itself, creating an opt-in system to remove copyright using existing laws.
In short: copyleft only depends on copyright because it has to, and it only has to because it's a minority position. Actual GPL supporters would be perfectly happy if the equivalent of the gpl was law and normal copyright did not exist.
As its not enshrined in its own law, in reality it does depend on strong copyright law.
Some contributors that you know - perhaps the majority that you know - may be shaky about this, they may not understand this, but it doesn't make it false and nor does it mean that other contributors are ignorant.
In short: copyleft only depends on copyright because it has to, and it only has to because it's a minority position. Actual GPL supporters would be perfectly happy if the equivalent of the gpl was law and normal copyright did not exist.