People are wondering today whether Palm (PALM) CEO Jon Rubinstein is a “liar or a fool,” to snatch a phrase from The Business Insider. That’s because Rubinstein said last Friday he’s never, ever used an iPhone.

“I’ve never used one … it’s the truth,” Rubinstein told All Things Digital’s Kara Swisher during a Q&A at the Consumer Electronics Show in Las Vegas.

What an odd thing for an ex-Apple exec to divulge, especially since he now heads a company that’s trying to compete directly with the iPhone.

Of course, if Rubinstein is telling the truth, such a lack of dabbling in a rival’s pool could explain, at least in part, why Palm is having a hard time catching up to the iPhone’s market share. The Palm Pre has fared so-so at Sprint Nextel Corp., despite a lot of hype surrounding launches of the various iterations; and the more budget version of the Pre, the Palm Pixi, appears to have made little splash. Palm is due to start selling handsets through Verizon Wireless.

And if Rubinstein is fudging, and has tested the iPhone, he still made himself look ridiculous. Palm could take a few cues from Apple’s success. For instance, Palm has just more than 1,000 apps to offer its users. Apple boasts more than 100,000.