That's more like it!
With Chombo, the American influences were the branches. The roots were in Cuba, in the clave, the son, the Cuban articulation of the Spanish language (and that's a whole 'nother game right there, Cuban Spanish...). The cat was equally adept playing violin in a charanga band as he was playing All The Things You Are with Mongo. And the more one becomes familiar with the more "native" influences, the more distinct the character of his playing becomes. A lot of "homework", to be sure, and ultimately it might only matter some, but...it's there for the taking if one is interested. Cuba is not a secondary world of music, it is a fundamental, one of the world's primal sources.
I'm a big (enough) fan of melting pot, but melting and erasing are not the same thing and should not be confused (not saying you are, Larry, just making a general statement). I know Marty Holmes' work with Puente, it's fine, same with Brew/Machito, but they both definitely sound "American" at root, whereas Chombo does not, which is as it should be, I'm just saying that Chombo = Marty only in the sense of good tenor players playing in "Latin" bands.