I think I want to answer this in a little more pithy fashion.
1. If you are willing to use last 3 months, you are overpaying, because it should be trailing 12 at least, and it should definitely be the same time period as the one you use for expenses or it is an apples to oranges comparison. That may be fine if you are buy and hold and everything else is in place, it is for you to decide. Some seller's are attempting to use 3 months, but I personally think every buyer should resist and even refuse this.
2. If the previous manager really committed theft and fraud, there should be a police report, shouldn't there? If not, at the very least back to trailing 12 it is.
3. I would check credit scores and criminal background check all these tenants they managed to miraculously add. Some owners will lower tenant standards, hide concessions, etc. (as others have been pointing out to me in completely unrelated PMs) using mgt fees, maintenance expenses, anything they can think of to hide them. NOI looks up, but Caveat emptor. 6 month leases might be part of that.
So those are the things that make me hesitate, but I do not wish to distract from the positive points others have been making. This may be best you will get in the market where you wish to purchase. At the same time, I would beef up due diligence even if it costs a few thousand more.