Well, we are 15-4 in the previous 5 tourneys and we missed the sweet 16 once. Remember, basketball is a tad more unpredictable than football, especially since the addition of the 3 point shot, so the best team does not always win. The championship team with Manning on it really was not that great, but they won, so it sort of averages out
The Helms titles were legit, they were the main organization to get one from in Basketball before they had the tournament. Those were legit teams too, I think it is really the only "championship" anyone claims pre-NCAA, at least to my knowledge. If you go to the Tar Heael's website, they are also happy to cite their 1924 Helms National Title, so it's not like we just made it up and other major programs ignore theirs (although I am not sure what all other programs think, I checked UNC because they have lots of titles).
Anyhow, we have a good team this year, we are around the 4th to 8th best team. If we win it, it may not be that we are the best, but if you keep getting good shots at it, you will take some titles. That is just how a single elimination Basketball tourney plays out...