Mark,
To say the US Open means nothing outside the US is just, well, dumb.
To his discredit, Trevino skipped a few Masters Tournaments during his prime as he didn't particularly like the atmosphere there. I think it was Nicklaus and some others that persuded him to quit skipping the event.
While the PGA may not have as much prestige today, it is a fact that the four professional majors since at least 1960 (when Palmer revitalized an Open Championship that was itself becoming marginalized in importance) are (in order of age):
The Open Championship
The US Open Championship
The PGA Championship
The Masters Tournament
Seve knew damn good and well that the PGA and US Open were two of the "biggies"--he just couldn't win them. Of course, Seve showed great imagination and genius in winning at The Open and The Masters.
But, Trevino's winning of the Open also cemented his greatness and he also won US Open and PGAs mano a mano against (to date) the greatest ever. Yes, Trevino did not win a Masters but couldn't one say Seve "only" winning Opens and at Augusta showed he was kind of one dimensional--i.e. he couldn't win on on a course that demanded different strengths--driving, patience, strong mental toughness?
Also, did Trevino ever have a choke during the final round of a major anything close to Seve's collapse at the '86 Masters???
And as for longevity, Trevino at almost 70 today could give Seve 3 a side TODAY and whip his ass!!!
(Just a question but I wonder how many Masters Seve would have won on the "new" tighter more tree-lined Augusta?)
Anyway, both are greats and I can see someone favoring Seve over Trevino but to suggest the US Open and PGA don't matter is, well, you know...
PS Since the US Open and PGA don't count are you saying Jack has only 9 real major professional championships?!?!