The scientists likely have exact records in their lab books etc. But there is no animal-accountant running a single, company wide, exactly accurate MI dashboard...
In companies I've worked for there very much is an "animal accountant". They are also the "cadaver accountant". You can't just throw those things out with the morning trash, you can't just buy them on Amazon. You need permits, permission, documentation.
Well you also need to house the mice and do what you can to avoid unnecessary discomfort. In that process you will certainly be doing accounting to e.g. ensure you have enough cages and that they are being cleaned at a proper frequency.
You will also be justifying the study protocol and as part of that an intended sample size. Sure if a mouse gets killed accidentally by a shaky undergrad it's not a major event, but you also can't just kill an order of magnitude more mice than the approved proposal without getting additional approvals.
There are strict rules about this at every university I've seen and I imagine they developed because of government grant stipulations rather than out of the goodness of their hearts. It's a legit cost - vets need to be on staff and individual labs can be fined for breaking rules. I'd guess biomed companies end up with a similar structure normally due to how closely linked they are with the rest of the research machine.
Having these centralized housing areas for mice from different projects, in addition to the IRB records of what was proposed, ought to give a pretty accurate number of mice on the department level. If the government asked for it to be calculated, I'd be shocked if the university didn't quickly turn around with a number.
Regardless, it is bad scientific practice to not document the number of mice used. It's not even an animal welfare thing, you should be documenting the number of petri dishes you look at too. Not doing so could easily enable sketchy behaviors like p-hacking as well as increasing likelihood of honest mistakes.
I'd also hope at a company like Neuralink they have electronic lab notebook functionality that would make it straightforward to pool numbers across individual researchers.
Personally I didn't find the 1500 number so outlandish, as I assume Neuralink is targeting a very broad scope. However some of the other details certainly raise red flags about their operating procedures.
Have you worked for a company or can you cite other experience beyond the person you’re replying to? You sound needlessly skeptical about a claim you actually have little knowledge to evaluate.