These may be of interest to you:
There's two schools of BGz in my opinion. The school of thought where they are there for presence and smoothing over as a technicality, and the school of thought where they are the expressive glue holding the film together and responsibly for breathing life 'off the page'. Neither are wrong or right, just different points of view on BGz. Personally, I'm in the latter school.
In the mix, BGz tend to play very low except for a few circumstances where it can pop through without fighting against other sound elements (Jurassic Park and Contact are a great example of this - the BGz are very lush and full of depth and character, and there's many moments where they are allowed to breath with no dialogue or music going on). That's another reason I like to support the idea of being appropriately bold and expressive with BGz, since this may be the only 'saving grave' to really allow it to pop through a mix tastefully when everything else is going on.
But the ability to do this comes down to time and budget, so many times it's finding a happy medium and picking your moments to go big, and knowing where you can go simple.
For Family Guy, I'm pretty sure sure there's a BGz pass (given that Todd-AO does the post) but it likely plays very low, and I'll bet the way it's played as an aesthetic choice. Nothing like the funny 'crickets' awkwardness moments when we hear the birds chirp over the house or the zip zip buzzing of the Drunken Clam sign. With VO too, the recordings are going to be clean, so you don't have to worry about smoothing over and masking dialogue issues with BGz (as we sometimes do using mono airs/winds/roomtones to help backfill trouble), so in a case like this show, you can get away with being quite stark and it doesnt affect the final product.