Training bizz is a HUGE money bizz..

You should have money set aside for litigation.

If you can get a better primary residential HELOC rate than you can a hard money bridge loan I would say yes.

By using the BRRRR strategy, you only need to put down money once.

Based on what my real estate agent thinks that this quote will be, roughly, and the after repair value, it looks like I could buy this property in cash, spend a month or two fixing the damage, and then put a mortgage for roughly 1.6x what I paid for it and thus have a cash flowing property at a few hundred dollars per month and a little more money in my bank account ready for a down payment on the next deal.

What you’re suggesting is not cash flow, it’s return of principle, giving her her own money back  If she sells with your deal.

Rents started to come down and I had to leave a lot more money in projects that I was in the middle of.  

To answer your question directly OP, to sell a deal and make money. 

They loved it because they got some play money right away and steady income each month without having to deal with toilets and tenants.

The refund part is just to get you get committed to another deal that makes them even more  money than that refund.