At first I was thinking this just seems like another timeshare scam wrapped up into a different, more deceiving package but after speaking with the agent they assured me that after purchasing the fractional share, I would be deeded 1/13th of the property.

Requesting documentation for any other reason may be considered discriminatory and a violation of the Fair Housing Act.Review state and federal laws: Familiarize yourself with the applicable state and federal laws regarding tenant privacy, anti-discrimination, and fair housing.

Based on what you are saying I think the scam is the person who is contacting you on IG. 

Just like all the scam phone calls we all get, they must work on some level or someone would not be doing it.

I tried one before from a different realtor but everything sounded fake or like a scam almost so I did not go through with that one.

If you really like them and want to move forward, ask for a larger SD, do employment and prior landlord reference checks.In Chicago, we're seeing a lot of scams with people applying for apartments with a friend's name and income.  

People who are lying to you (or scamming you) right from the start when they are (or at least should be) on their best behavior, are going to be more of the same if/when you rent to them.

People who are scamming the system and it is a problem for all of us.There are other ways to help pay for expenses, like SSI supplemental.

Is this some kind of a scam?

As a reference we have about $50M of AUM so I am not some wingnut anti home ownership person