Did Eero Saarinen design these Knoll swivel chairs? Are they even Knoll?  

pics

No, these are not a Saarinen design. They have the same general shape as the Saarinen chair but that's about it.
The wood base has a clunky look. I think wood was used in this way to give modern-style office furniture more warmth without straying into the totally traditional antique-ish look that a lot of office furniture places were (and still are) producing. Also, the wood on these chairs looks like a common light-colored species with a walnut-tone finish on it. I'm pretty sure that Saarinen didn't go in for that kind of thing.
This chair shape was widely copied, by the way.

would I be correct at least by saying/listing these as Knoll chairs?
https://www.1stdibs.com/furniture/seating/office-chairs-desk-chairs/knol...
Others seem to think they are...
and has anyone ever seen these bases on a Knoll chair?

That's not the same chair, Knoll or otherwise.
Using the ball casters as a guide for matching the size of these two photos exactly, the following differences become obvious:
1. The top of the back of your chair is broader and more squared than that of the 1stDibs chair.
2. The angle where arm meets back is more acute on your chair than on the 1stDibs chair.
3. The seat on yours is wider and thicker than the one on the 1stDibs chair.
They're similar but not the same. And again, there are lots of chairs with this same basic shape, both vintage and contemporary. If you can find photos of a chair that matches yours exactly in all these subtle details AND that has original (i.e., non-faked) Knoll marks and/or labels, then sure---it's a Knoll. But without that kind of provenance, you would be really pushing it, I think.
Or, you know. Write to Knoll and ask. I can't remember if they are one of the ones who are good about responding or not. Maybe they are! Good luck.

These chairs have been recovered. I thought maybe the upholster maybe got crazy with the padding a bit. I got the chairs from a local auction. There was a handwritten note on the bottom, it said purchased in 1974 recovered in 1991. Thanks for the input...I am kinda leaning toward these not even being Knoll also. Like you said the only thing I really see in common is the Shepherds Casters that you do see on Knoll Chairs. The only thing that I can find a mark on is on the wood coverings over the x base. They are actually molded plastic with wood veneer. They slide right off, and they are stamped DAVIS?

Shepherd Caster is a big company that has supplied casters to many different furniture companies for decades, so that isn't something you can go on.
The veneered plastic covers on the base do not sound like the kind of thing Knoll would ever use on anything. I think you should just list the chairs as mid-century modern office chairs and leave it at that.