Sometimes it's written "Du" even if in the middle of the sentence when addressing someone directly. It's technically incorrect, but it's used for emphasis and hence politeness, and that's probably where your feeling comes from.
The same can happen with other words that are getting capitalized for similar reasons, but when going strictly by the book it's grammatically incorrect. An example would be "das Große Ganze" where it should be "große" but it is capitalized to emphasize the connection/phrase.
That's wrong, it's not technically incorrect. In fact before 2006 the only correct way to address someone personally in written form was to capitalize the Du / Sie / Ihr. Since then you are allowed to write it either way. I still use the capitalized form because I'm old and that's what I learned back in school.
> Since then you are allowed to write it either way
Okay, my interpretation is that it doesn't really make sense within the language rules, so they changed it but allowed to use the old style to make the transition easier. ;-)
> I still use the capitalized form because I'm old and that's what I learned back in school.
Impossible to keep up with all the Rechtschreibreformen anyways.
It must be so cool to see all of them "from the top" (i.e. someone who has been natively-and-highly educated, immersed in the language for their whole life); but it's from the outside it's like a fancy club that you just can't seem to get into :)