That exact thing happened to me a year and a half ago. The engineer asked if I would play a Fender he had there instead. In fact, he just assumed I would do it when he asked. I told him I didn't want to and stuck with the Gibson throughout the entire recording session.
Engineers (live sound guys, roadies, guitar players) have a preference for specific gear because it makes their job easier. I know one guy who insists that there is no need for amplifiers onstage (or anywhere else) because PA systems and recording gear have gotten past "all that". Fightin' words. He was visibly repulsed when I mentioned using an SVT... miked no less. The P-Bass has a comfort zone that covers a large spectrum of popular music and sits nicely in a mix. Fine. Unless of course, your music was created around the sound of an EB-0, or a Rick, or a Thunderbird. So whenever I go a-recording, I bring the bass I need - plus a Fender of some ilk. At least it's MY Fender.
