See https://www.hq.nasa.gov/alsj/a14/ap14-KSC-70C-156BW.jpgThat is the Apollo 14 MET with clear goodyear logos on the wheels. The rover wheels were designed and built by GM however.So the claim that Goodyear put wheels on the moon is correct, they just weren't the rover wheels. Given that most would be unaware of the MET, I expect that a more immediately recognisable iconic image was used for advertising purposes.
Many thanks for your responses - it would appear Goodyear are using a little poetic licence with their advertising.Wishing you all a happy new year.