I didn't want to pay for premium services, so I changed my method to paying by credit card instead of out of my return, then got charged for premium services anyway.

It sounds like you are a California filer that originally chose to pay the TurboTax fees out of the Federal refund.   In California that invokes Premium Services and a 39.99 fee.  I assume you later changed payment methods without properly removing Premium Services first. 

I realize it won't help you now since you already paid, but here's how it normally is removed.  It might help someone else who sees this thread.
https://ttlc.intuit.com/questions/2154391-how-do-i-remove-the-premium-services-fee

You'll need to phone TurboTax Support during business hours for assistance with any fee/billing issue.

Same here! I tried very hard to not fall for the frequent interruptions to buy more stuff, upgrade, etc. and then when I was done, it said I had paid for premium WHICH I DID NOT WANT. I think they are counting on you being fatigued after all the hours of entering numbers etc. Yes, I'd like to be refunded for the extra I paid.