My career is in animal behavior and training though I do not have professional experience with parrots. I do live with a parrot, and as any owner can attest that is quite a learning experience - but in the big picture that does not add up to a whole lot.
Chet Womach seems to be a highly skilled and qualified trainer but the claim that you will see results in fifteen minutes is just absurd. This was likely made by some marketing nutball with no knowledge of training, or if it was Chet's statement then it is simply dishonest. With the right techniques pet owners are often amazed at how quick and smooth training can go - but it does still take time.
I think we have a few members who have used Chet's videos, perhaps they will comment on them, but a few things to consider:
1) General purpose "cookie cutter" training methods have very limited application. If your bird is perfectly well behaved and you just want to learn how to teach a few tricks or activities I suspect you could get quite a bit out of the videos. If on the other hand your bird is a handful, as most are, you need techniques tailored to your bird and your situation. If you ever get a chance to work one-on -one with Chet Womach TAKE IT, but I would not be so quick to jump for the videos. One size fits all never fits anyone.
2) Be careful ordering online. Apparently there are MANY 'distributers' of Chet Womach videos; quite a few of them are scams - you'll pay but they wont send any videos. This should not reflect on Chet or his training methods, but for whatever reason his name is being used as the pitch for many online scams.
3) I just had to include a three, because a list of only two is just boring

Oh yeah there is a third point - you can get most, if not all and some more, information you would get from the videos on forums such as these... for free... and tailored to your situation.
So all in all I don't wish to dissuade you from buying the videos - but consider the reasons. Is he the "best"? well thats a bit subjective, but considering all the trainers out there I'd say such a claim is a best arrogant but more likely an exaggeration or just a lie. Is he highly skilled and qualified? I believe so. Will you see results in fifteen minutes? No.
If you have a well behaved bird and you are just looking for some activities to do with him/her and hope to teach a few fun tricks and you have the money to spend then the videos may be just what you are looking for. Otherwise there are likely better ways of achieving the goals you have with your parrot.