How far would an Ivy League probe an applicant's internet history?

Hi,
I’m applying to Princeton and Stanford in the fall and I was wondering-do these schools have reputations for doing extensive research on applicant’s social media? The reason I ask is this: Although there is absolutely nothing on my Facebook or Twitter accounts that I’m ashamed of-they both are very clean and have no suggestive/partying/immature photos or comments on them-a few years ago when I was a freshman, I took an online class ( one of the classes they have available to the public) with one of those schools I listed above, and, in the chat forums, made a few mildly immature comments that could offend some. I’m not talking about racism or sexism but just rather some politically controversial remarks I now regret. I have been unable to find this forum however as the site was archived, meaning it’s no longer accessible to the public. Is it likely or even reasonably possible they would find this forum and hold those remarks made several years ago against me (in the application process)?

I think the admissions staff will have better things to do than seek out something that is not readily available via a google search

No. You seem to overestimate the amount of time admissions officers at colleges that receive 30K+ applications have on their hands.

They won’t find that. Nothing to worry about. Glad you’ve grown up some.