The fallacy in your argument is that Martinez has never come out and said that he rates Welbeck, so I'm not using his "expert knowledge" as a basis for my judgment of Welbeck. Jelavic was poor before Martinez (as evident in his last season and a half at Everton), as was Anichebe (all of his seasons here). Vellios apparently just didn't give a damn.
I said I would trust Martinez IF he acquired Welbeck, because so far his signings have worked for us (bar the injured).
I took issue with the fact that you think Everton would "drop like a stone" because of one player. I think that is ridiculous statement, and when you claim to that you don't want to stoop to our level (but do anyway), that is extremely condescending.
The funny thing is, is that if a highly-rated manager came out and agreed with YOU on Welbeck, then I could assume that you would be appealing to authority... or would you not, since you're apparently an expert, too? There's some fallacy for you.