There are two ways to know whether you're in tune or not.
First, you can do what Melissa Cross calls 'singing above the pencil' - basically, using your head as a resonant cavity (as there's plenty of free space up there for the average singer) - and this will allow you to hear yourself very well. I suspect that he's doing this.
Second, you can have the ears blocked so that your voice seems to be 'pushed' there, and then refer to the dampened surrounding noise to determine where you need to be singing - I suspect that you're doing this.
What needs to happen in either case is called 'audiating' - imagining the pitch perfectly an instant before the note comes out, as if you had a piano in your head (might want some Tylenol, making those fit is never fun) playing the notes. Otherwise, you're 'climbing' up to the note and this, while usable on occasion in case of fuckup or for added emphasis on a note, gets very annoying after a while. Doing. That. Every. Note. Is. Like. Accenting. Every. Word. As. If. It. Came. From. The. Heavens. And. Needs. Its. Own. Sentence.
In either case, different people need different things - neither of you should use the other's method if it's not comfortable for you. Hell, just to shut the argument up try recording a sample from the songs live and running them through a tuner to see how much the needle wiggles. Either way, you need to do what allows you to perform better, regardless of what others say (provided you're not just being ignorant, stubborn, and arrogant), and not use that as an excuse for being 'off' in any situation.
Jeff