It was also raining pretty hard while I was there and it was dry so it's most likely not from the side of the house and the roof would be a long shot to flow around the floor above it and just end up there. 

Or am I stuck with this self inflicted gun shot through the foot? 

You're not the boss here, you don't call the shots. 

“You get one shot to make an attractive offer package,” Platt says.

They gave it a vitamin k shot, and sent it on its way with scheduled follow up appointments.

Below is a hypothetical screen shot of various line items in a typical NOI calculation.

Once I purchased a different primary residence I knew I wanted to rent out this property & give being a landlord a shot.

One wrong item comes up, wether it's a structural or foundational issue and your deal could be shot. 

The fact that this was their counter, makes me assume you have a good offer by a long shot and so have some room to negotiate.  

It's the same way a bar makes money: They buy whiskey by the barrel and sell it by the shot.