No only is your dealer lying, the act of voiding a warranty because of where you have it serviced is illegal.
I have free oil changes for the life of my Prius at my dealers, one of the reasons I bought from them. They have their prices for service compared with the quick oil change places and other garages on a big sign in service and they are right in line. This is the first new car I have bought that I did not have to go back in a few months to have things fixed, like knobs falling off, trim pieces on wrong or missing, the door mechanism breaking so the door wouldn't open, etc. I'm impressed after my other cars.
Maintenance has been very inexpensive so far. I have 126,000 miles. I've paid for: - new tires at 65K - Mobil One oil change every 5K to 7K, mostly done by me - 3 sets of wiper blades - 4 air filters - 2 cabin filters - 1 side marker light bulb - 30K, 60K, 100K services ($200 or so each) So maybe I've spent $2000 in the past 4 1/3 years. Oh, I've averaged 48.4 MPG, so gas costs are really low too.
Maintenance? We don't need no stinking maintenance! 63,000 + miles, never been back to the dealer...for anything. Oil and filter changes are easily DIY, or any competent service guy. I rotate my own tires at 10K (recommended 5K), and still have original tires at over 63K. It is the MOST maintenance free car I have ever owned, including a couple of almost bulletproof Subarus. Maintenance problems because its a hybrid? NO. Not to worry. Drive it a couple of hundred thousand miles, and let the next guy buy the battery replacement.