As you, in my opinion pushed your responsibility onto the tenant to contact the HVAC company and there is no indication you spoke with the HVAC company prior I think any misunderstanding is on you.  

If I'm misunderstanding something please tell me that's why I posted this question

That might be a way around the 'lender' and setting up an equity share agreement with your parents may help you avoid any estate misunderstanding problems with siblings down the road. 

It's always best to put everything in writing so that there are no misunderstanding that lead to a lawsuit.  

Or am I misunderstanding something there?

You should put some kinda agreement in writing witht he owner so there are no misunderstandings in the future.A one bedroom apt over a garage will likely not rent for much per night.

Bruce, You seem to misunderstand my point. 

Or am I misunderstanding your quote?  

Unless I misunderstand how it evolves at that point. 

If it's a home-run and you want the place then a simple letter to them apologizing for the misunderstanding and recognizing how much of a nuisance it is to have your home traipsed through by investors (especially during a pandemic) is.