In fact, their operations -- in as little as they've been made public -- have been pretty opaque and sweeping (i.e. not detailed, as in transparency), and what little we have seen of their analysis techniques seem to be shallow and unconventional (i.e. not formal and measured, as in auditing).
I'd warn you not just take what public figures say at face value. Transparency and auditing are indeed virtues to strive for in governance (and we have many running systems for those already), and maybe they'll someday reveal that they're actually contributing to those virtues themselves. To date, they have not done so.
Doge is using a sledgehammer when they need to be using a scalpel. There's already been so much chaos with things like federal disbursements being frozen then unfrozen, firing and rehiring employees, moves being blocked by courts due to being unlawful, etc. You can't "move fast and break things" with a trillion dollar bureaucracy, people's lives are at stake and something might break catastrophically.
I also don't trust Musk with so much power because (1) he's an ideologue and (2) there are numerous conflicts of interest. I am skeptical he would be held accountable for any potential wrongdoing in this political environment.
We all should know the way this is being done is wrong and it will either have to be removed or redone, which is equivalently costly and might as well be the same thing at the end of the day.
I would expect the same practices from all of you in your own day to day work. We expect it from each other.
The lack of transparency is enough for anyone here to worry. It bucks every best practice and is a red flag in itself. We do not accept this in our work - it is what we all value and that has to be the north star.
This is why I do suspect their intent. They are not walking the talk.
Where are the forensic accountants? Who uses CompSci-track college kids to audit billion-dollar orgs?