I was wondering about Insignia too, after seeing the 20" TV for $58.99 after rebate, so I searched around and found a review of another one of their TVs on eOpinions. I don't have enough posts yet to post the link, but at eOpinions, just search for Insignia and scroll down to Electronics. One of the TVs (actually, I think the same TV that's being sold on BF) was reviewed.
Apparently, Insignia is just a Best Buy brand of TV that's built by other (reputable) companies and slapped with a different logo. I guess it's like the store brand food in supermarkets, where it's the same food, only cheaper.
I would think that it'd be okay to get the Insignia without any qualms whether it'd break down, but then, I won't know either until I get the 20" either. :-p