That doesn't mean there aren't people and situations that it is ideal for.

That said, I would love to be able to get the tenant out so that way I can completely rehab the place, bring rents up and get someone in both sides that I approve of (I don't think they would pass my screening process).The situation I'm in is this...Owner of the house passed away (I believe) and left it to her daughter that lives in California. 

 Just wanted to add my two cents here as I did review a similar situation with @Jay Hinrichs a few months back.  

My approach would be to buy the one and feel out the situation. 

Sounds like you bought a house, with taxes paid up for the quarter already and you took possession sometime during the quarter. it also sounds like they forgot to calculate the tax credit due to the seller at closing. if that's the case, I believe most purchase contracts have a clause that states you will make it right if there was some miscalculation or simple omission at closing. even if not, the old owner paid for taxes and you are benefitting unjustly. the ethical thing in my mind is to refund the extra tax. there is no reason to go to court for this.if i'm wrong, please explain the situation better.

We did that as well when my wife and I started our real estate journey. 1) If she is signing a longer lease, I would actually increase the rent slightly and say that you will not have to worry about us raising the rents every year and that it will actually be give you and her a more predicable situation as she wont have to worry about her rent being raise in a year and her having to find a new place. 2) Personally one of the hardest things to do when we turned our primary into a rental was to let go of the idea that its "our home" and its now a business.

The 1% rule is a rule of thumb, like you said, which means that it will not apply in all situations.

In my situation, would it make sense to put 5K down on properties where rent covers expenses?

“The thing that threw me off is the bank kept saying everything was still in in good standing.”Like many in the same situation, she was forced to move elsewhere.

They are very easy to get ahold of,  and a call to them explaining your situation might be of help.