I'm not a medical professional so I don't know the ramifications of letting an infant watch 20 minutes of children's programming a day, but I personally do not have any problem with it. I'm sure in the scheme of things, my kids watched more than 20 minutes a day at that age just by being in the same room with the tv on that someone else was watching.
I was a SAHM with my daughter until she was 2 and I remember watching Sesame Street and Nick Jr. with her daily. We'd watch the shows together and I'd try to build on the lessons that were taught as part of the program so we'd get something educational out of it in the process. She was later nominated to the Talented and Gifted program at her school in first grade by her test scores as well as by her teacher so I'm guessing watching tv didn't hurt her too bad. Of course, someone could argue that maybe she'd be a prodigy if I'd not let her watch tv at such a young age :-) LOL!
There are so many ideas about tv watching and I think it's like everything else - ok in moderation. If it seems to make your baby happy, and it helps her to fall asleep, and she's only watching a small amount per day, and it's rated Y or G or whatever the youngest age rating is of course, if it were me, I would have no problem with it at all. That is, of course, until they come up with some scientific proof that it does some physical or psychological harm in the long run, but I've not heard anything definitive about that as of yet.