"I found a bunch of responses that said owner's draws were taxable not on the schedule C but on their personal income taxes?"

Those people are wrong. I teach it this way: For the Sched C person, you are your own business. Everything is already yours. Taking the money out of the business, or not, is not the taxable event. Making money is the taxable event. What you do with it is up to you, because once you report that year's business operations on the Schedule C, it's already yours and already taxed.

Just a note: this is one of the things Dave Ramsey often gets wrong, when he explains this to his small business listeners.