I think this is where we should look for the answer, but it's hard to say. Jordan kept this vague for a reason, as every clear answer you give creates consequences for other aspects of the magic system, and as a writer you want to have a certain amount of leeway.
But there's other uses of the power that are also "talent-based": gateways, for instance. The weave is the same, but when Androl makes a gateway, he can make it really big, despite being weak in the power overall, but some channelers can barely make a gateway big enough the step through.
Though on the healing part, there might be more to it. In the current Age, it is common knowledge that healing is a certain exact weave, but when Nynaeve learns to heal, she feels like it's wrong sometimes, and starts to experiment a bit in using all five together rather than the traditional weave with just spirit, water and air. Nynaeve feels like the weave should be different for different ailments as well. This hints heavily at the Aes Sedai of the current Age simply not understanding healing that well.