I am planning to accept an offer as tenured professor in the US for some years (at least two). The university offices told me I cannot get a J1 visa and I need to apply for an H1b visa. They also say that I cannot claim the tax treaty benefits under the H1b visa. I've seen different opinions in the web. Also, from the official IRS documents it's not clear at all whether tax treaty applies under H1b or not. The mysterious thing is: anybody I know has exploited the treaty (even on tenure track), anybody known to anybody I know has exploited it. Can anyone help me out?

The H-1 and H-1B visas are WORK visas, so you CANNOT claim any treaty exemptions under such a visa.