Have to throw some doubt into this. A lot of research (much of it by Beth Loftus, whom I knew back in the day) has shown how easily memories can be made up. In fact, every time we recall an event, we change it to some extent in the process; memories are not static, they are constantly changing. Conflating events like this is not unknown by any means.
Because Froome was an adult or near adult when the event took place, and because he's only about ten years beyond that event, I would have thought the memory would be better. But remember Basso was in the Tour every year from 2002-05, and even in 2002 he was hardly a nobody. He finished 11th, and was the white jersey. I can't access the detailed information from that Tour, but is it certain he never challenged LA on any mountain stage? Even if not, the name might have stuck with Froome, then later, when he saw or learned about the 2004 and 2005 races, that information could have been stored and conflated with the earlier memories.
At worst, if this is a lie, it's just one to make the story better, maybe as in the book Three Cups of Tea. Whether it should be regarded as evidence that he lies about everything is questionable. In any case, there is enough evidence of other inconsistencies in that interview that it really isn't necessary to spend a lot of energy demonstrating that he lied about this.