>>1 You cannot help someone that does not want to be helped. Period. In fact, while you feel that what he said is untrue, it IS true to him. And it makes it all the less likely he'll turn to you should he really need your help.
No one dealing with depression WANTS to deal with depression. Don't take it upon yourself to help him with his problems, just remain open to help him should he ever need it of you. Stay close enough to observe if any major red flags arise, but ultimately this is his battle to fight.
One of the thing people don't like to acknowledge when dealing with mental issues like these is "just talking to people" may not be a good choice. I'd recommend him discussing things with a professional, and go from there.
Otherwise, relax. Don't feel the need to change your relationship with your brother just because he's "your depressed brother". That doesn't matter, he should still just be "your brother" to you.