I could be wrong, but based on the examples of dandelion and thistle, the current name of Compositae is Asteraceae. Current family names of plants end in -aceae. Asteraceae is a rather specious family with a lot of vegetative and floristic characters represented, I could see how it could be called Compositae.

I didn't realize the goldfinch's late breeding season, though, I suppose if I'd thought about it, it would have made complete sense :P