I've had to research this sort of thing for photography/advertising/graphic design work, I'm in Texas so my research is generally related to state law here, but they usually all match up... Also, IANAL... But I am the son of one, and I've looked into a lot of this stuff. I'd still ask an IP/copyright attorney, but....

Typically the IP in question has to meet a few certain "tests". 1. Is the IP the focus, and what is being promoted?... Here it would be no, and it's for a movie. 2. Is the IP generally recognizable to the public. This is for something like if the main actor were wearing the batman suit and they were playing off of that to sell their product. Generally the "does Joe schmo recognize this" rule of thumb plays into it here. So you'd have to ask yourself if the general public would see that logo and think "ohh yeah that's totally that one guy's shirt design." If it's merely there and not essential (would the ad be different if if we're a design I did?), it's not really something that will get any traction.

As for why are things blurred? That's been properly answered... Protect promotion / product placement value and cya for product association.

Why would cbs contact ahead of time? Probably just so they don't have to deal with it later and so they don't get bombarded with claims from tons of different episodes of shows. Also some production companies might just worry about it a little more. They have to worry about different mediums in different ways. Music, for example, is different because it contributes to an essential emotion or feel of the work. Think about if something is filmed in Times Square, there's lots of random logos and such going on there. Eh, whatever. But lots of 30 year olds remember what song was playing when Emile Hirsch finally kissed the Elisha Cuthbert in The Girl Next Door.