I am not a lawyer, but I have gone through a software audit before. The following is based on my experience:
BSA won't care if they're using the same license keys, as long as you have enough licenses of the correct type. In fact, when you do volume licenses you buy a bunch of licenses at once but only get one key. The next time you buy another batch of licenses you'll get another key, but you can continue to use the old one.
The only thing that they'll check for in a licensing audit is how many of each type of license you have, and compare that to how many of each type of license you own. Keep in mind though that when I say "type" of license I don't just mean "product". For MS Office there are multiple SKUs (Standard, Professional, Enterprise, etc) and multiple ways to obtain (OEM, Volume License, Retail, etc) and they do track those separately. I bring this up because you might have 100 volume licenses of Office Pro, and 100 retail installations of Office Pro, and you would be out of compliance. The same goes if you're licensed for Office Standard and have Office Pro. On top of that, there are also evaluation versions of software that you can get dinged for. I had that happen once too.
Keep in mind that when you true up, you're not allowed to uninstall/reinstall to make you right, you have to buy whatever it takes to cover the gap.
This is one place where volume licensing really helps. You can track all of your volume license purchases through the MS eOpen site and have an easy way to find out what licenses you own. Unfortunately most people don't know about volume licenses, so they start buying some retail licenses, then some OEM stuff, and when it comes audit time they have no way to easily prove what they own licenses for. I've spent a lot of time tracking down purchase orders that were from three years prior because the previous staff didn't buy volume licenses.
The following is my personal opinion, and may be completely wrong (though I think that it makes sense):
All that said, I think that you are mistaken about your licensing. If you lease PCs from Dell then you're responsible for the software installed on it (regardless of what came preinstalled) because you are using the software in your business and Dell has no way to know how you are using the machines (nor do they care, so long as they get their money). If you look at your client's situation from that perspective, the former owner is "Dell" and your client is the company using the machines. It seems pretty straightforward in that case. But on top of that, there may be some language in the licensing agreements that prevents the rental/leasing of the application software (or at least put limits on how it can be done and by whom). The former owner of the business may already be in violation of the licensing agreement in that case.
Unfortunately, there's no way to know for sure until you go through an audit. That's the problem with BSA/MS audits. There's so much grey area in software licensing that no matter how strictly you manage it, you're always going to have a gap between what you have licenses for and what you have installed (unless you use all open source or something like that). Your only hope is to minimize the gap as much as possible.
On the bright side, the "software police" aren't normally interested in going to court to try to get damages plus fines. They know that practically every company in existence is out of compliance, so if they get you to buy enough licenses to true up they're usually happy.
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