The tenants just called me saying they have a notarized rent to own contract signed between them and the previous owner and all of his receipts showing that they have paid every month.

Oh, forgot to add that to file in the public records, the signatures must usually be notarized.  

Quick Update:  for anyone planning on moving from your primary residence (which I am in the process of doing), the process for Chicago properties is to fill out this form online, get it notarized, and  mail it in the to the County Treasurer:https://www.cookcountytreasurer.com/nameoraddressc...You'll need your property PIN(s), which should be easy to find. 

I would however suggest to have it notarized to be able to prove the date of the assignment if challenged later on.Don't forget to notify your insurances to reflect the change of title ownership of the properties. 

I am in Idaho and the only time I've paid to have anything notarized was when I was in Louisiana and closing on a property in Idaho, had to pay a notary a few hundred bucks to notarize the closing docs.

If we are discussing a cash buyer then it's not likely anything needs to be notarized... therefore the transaction can be done 100% remotely (print, scan, email, fax) and payment can be made via wire transfer. 

Do all contracts for buying and selling need to be notarized every time?

I think they should have renters submit some type of notarized lease and give up to 50% additional on top of unemployment to cover rent: End of story.

However, there are some templates on Google if you search them and I think you could craft a simple one and have both parties sign/notarize.

Although it's true most SFR are pretty placid, the times when they are not are definitely anxiety-inducing, I agree.