I was referring to major label studios like Columbia that record big name acts that actually have contracts and recording careers!
It doesn't work like that anymore. Up until the mid-1960s, a band or artist with a Columbia (since you cited it as an example) record deal went to Columbia studios to record their album. The producer and engineering staff would've all been employed by Columbia, and the band or artist wouldn't be in charge of any important tracking or mixing decisions; in fact, they'd likely never even enter the control room! The Beatles broke that "glass wall" as they began to accrue the kind of clout that empowered them to take a stronger hand in the recording process. George Martin, in that context, played an important role in developing the template for the modern-day producer, starting out as an EMI employee who told the band what to do, but eventually becoming a guiding partner with the band, more interested in helping them find ways to realize their ideas.
Today, the decision about how to record guitar is ultimately up to the producer and artist. The engineer has a say, but really, it's only up to the engineer to enable the actual recording of each instrument according to the producer's aesthetic concept for the album. The "studio" (whether you're talking about the actual facility or the label, though they are two distinct things) has no say in the process whatsoever. In fact, most major labels don't even have their own studios anymore. I've worked at A&M's studio, as well as the old studio in the basement of the "record-stack" Capitol building in Hollywood, and neither of the artists I was there for were recording for the labels that owned the facilities.
Generally, the way things are today, if a guitarist who's part of a signed band has been using the Axe during the writing process, the producer is probably going to at least give it a chance. Even the most old-school guys would likely simultaneously record both via the method he's used to--mic'ing an amp--and the one the artist favors, leaving the final decision to whichever sounds best during the mixing.