This is entirely consistent with his other lies. He doesn't say something that's completely false, he exaggerates or creatively interprets the fuck out of something that did technically happen.
For example, I've said to friends that I'm working for (well-known company A) on a major project, when in technicality I'm working for a partner company B to accomplish said project for A. I don't remember my exact wording, it might have been less misleading than I remember, but it was just way quicker to say the bit that I knew he'd understand all the pieces of instantly, not to mention I do have an NDA so I wanted to be picky about what I said. Point is, that's the sort of lie he tells... the sort of lie the evidence supports, as long as you don't look too closely at it.
except instead of being done just for convenience, he's taking that grey area and exploiting it to it's absolute limit.