Your understanding is correct: it was the success of The Guild and the timing of the writer's strike that inspired Joss to make his own thing.

By the way, if anyone here has managed to not watch Dr. Horrible's Sing-A-Long Blog, I can't recommend it enough. I also recommend The Guild, though if you only have time to watch one web series than the three ~15 minute episodes of Dr. Horrible are where you need to start.