Boiling Water For Pasta - With Lid On....Do I Have To Wash The Lid?

I hope this is an appropriate question for the site.

Today I was cooking pasta. To begin with, I filled a pot of water and placed the lid on top. Then I cranked the heat up until the water was rapidly boiling. At this point, I was of the opinion that the lid was still clean. I'd even argue it very clean, as it had been 'steam cleaned' and the high temperature would (in my mind) probably kill some germs.

A roommate of mine disagreed.

Is the lid dirty?