There may be some valid concern they have that I just can't think of (though I've worked with Li battery systems for my day job for 22 years now), but claiming a battery voltage is not stable (which in other places seemed to suggest it could just suddenly surge to a higher voltage and damage something, I grant that wasn't directly stated in the email above) just seems like a complete misunderstanding of how batteries work to me. This battery is dedicated to your split camera, not also powering other things, right?
I can see if the same battery is also powering a drone that the drone's motor loads will be much higher and can vary suddenly/frequently, and the internal resistance of the battery and inductive effects of the wiring can result in the voltage seen by loads changing based on sudden load changes, so in a drone-shared application I can see the value in a (U)BEC for the camera (assuming the BEC itself doesn't have issue with the sudden voltage changes). But if the battery is dedicated, or only used for other tiny / relatively fixed loads (like a GPS unit) then I can't possibly see why there's any reason for concern, provided the camera can support the whole range of the battery. But the battery will always start high and work down, there won't be any surges or the like when there aren't other things hammering it with sudden surges.
This discussion got me interested in looking at split cameras, personally I went with HawkEye cameras (I use the FireFly Q6 as a Mobius replacement), so I'm leaning towards the FireFly Split 4K cameras, though the larger regular model supports a range of input voltages (has an onboard regulator) while the Split Mini 4K requires a fixed 5V input, so I'd have to add my own regulator, and right now trying to decide whether to go with a 2S battery and a buck regulator, or a 1S battery and a boost, so I'll probably just end up ordering both from Amazon and playing with them since they're all pretty cheap.