There's probably a study to support whatever theory there is you want to believe in. For this particular one about tv, here's one:
I personally don't think it is true. But then I don't want to argue with statistics. However, the reason for my argument is that when the babies are asleep, they are usually in a pretty heavy state of sleep. The brain just blocks out pretty much everything. When my 2-month-old is asleep, it doesn't matter how loud and crazy her other siblings are (fighting, arguing or just playing), she will sleep right through it all. And the same goes to tv noises. She'd be sleeping on her swing with back facing the tv while the tv is on (which is somewhat rare during school days) and still won't skip a beat sleeping. ;)
I brought up three other kids this way. And all of them are doing just fine in school even as 2nd language learners. They keep up just fine and even excel with one or two other subjects.
The truth is, it all depends on what you do consistently all the time, not just "while the tv is one when she's asleep"... it's also the times when she's awake and if that she's stimulated by having someone talking to her... etc. And just keep doing it. She will be just fine.
What many studies don't do is taking other conditions under which these kids may have been brought up in -- are the families all from the same social-economic background? Do the parents have equivalent educational backgrounds, temperaments and enough time to spend with the kids... etc. Think about it -- in an environment where the tv is on all the time, is it possible that maybe the parents are too busy looking after the kids in general (hence parking the kids in front of the tv), and by doing so may have indirectly delayed the growth? But it's not necessarily the tv's fault... but rather the parents did not have the time to stimulate the kids consistently. And there are many factors besides just tv.
My 2 cents.