On first hearing that sentence it sounds completely unremarkable, but studying it more closely I can certainly see why you asked a question about it. "Either" would not be appropriate in this sentence, however. It is a tricky one, but I think it comes down to this - he is concerned, so he uses "too".Of course, I am concerned that young people shouldn't break into other people's cars, too.
- He is concerned about young people breaking into his car.
- He is concerned about young people breaking into other people's cars, too.
The bottom of this page has some more examples of sentences where it is tricky for non-native speakers to choose the right word.
Incidentally, to me it is not the use of "too" that is strange, it is the use of "I am concerned that...".
Normally we say things like:
- I am concerned that I will not be safe.
- I am concerned that young people will break into my car.
- I am concerned that students are not interested in my lessons.
But Stephen says he is concerned that young people should not break into his car, which could be interpreted to mean that the fact that young people should not break into his car is concerning! It is completely clear to me what Stephen means though, and I would not even have thought about it unless you asked this question and I looked at the sentence closely.
And one more digression for any students of English accents - Stephen is almost speaking in his natural accent but he is doing a slightly silly voice. Listen to the way he says "principle" at 1:34, for example. I think Stephen would normally pronounce that word more clearly.