The original Gracie challenge was for publicity for Gracie Jiu-jitsu. Sure as well worked from a publicity standpoint, nobody ever heard of Gracie Jiu-jitsu thirty years ago.The challenge was open to anyone, not specifically/only for people involved in kicking/striking arts.
The confusion over the challenge towards Joe Lewis is a common one, you're not alone. It was actually a challenge by Helio Gracie to Joe Louis, the boxing champion, back in the mid nineteen forties. Again, it was for publicity.
Royce Gracie challenged Mike Tyson to a no holds barred scrap in 1997, "anytime, anywhere". Again, it was for publicity. Tyson was making upwards of fifteen million bucks a fight at the time, he wasn't about to fight anyone for free. But the publicity actually worked, it was mentioned in the New York Times. (I always wondered how they pulled that off) Tyson had already lost to Holyfield at the time, but Tyson still had the marquee name. Some might say Royce was lucky, Tyson would have bit him like he did to Holyfield in their second fight. But Royce, had already been bitten, right on the ear (just like Holyfield/Tyson2) during his first UFC championship fight with Gordeau.
A lot of the Gracie challenges were the reverse of what most people think. People heard about it and came TO Rorian's school and challenged them. Which they happily accepted right there on the spot. Some of the guys that lost became Gracie students the same day. Jason DeLucia is probably the most notable, he also fought in UFC 1 as an alternate to fill time because all matches were short ones. (real short ones!) He had been a Gracie student for several years at the time.
As for Benny the Jet, there's all kinds of rumors as to what did and didn't happen, what was and wasn't said, I have no knowledge and won't speculate, especially since I'm a fan of both men. But as Elder has already said, The Jet was a student of Judo Gene. He was one hell of a Martial Artist, not just a kickboxer.
Bottom line in the Gracie challenge, at least to my experience with the family, was "do whatever you want, we don't care."