Service people usually know about this flaw because they have encountered it during their work experience -- most tenants (in my experience) have no clue how easily vinyl flooring can be damaged in this manner.I would be tempted to leave the floor as is, then at tenant turnover, remove the vinyl and install tile. 

I'm flipping a house currently (I'm pretty new to the profession), and I just recently found out that the old floor tiles are almost definitely asbestos tiles.

It was a complete rehab except basement floor tile repair." estimates included in report".

It sounds like this company quoted you to install interior drain tiles, not sure what other foundation issues you might have. 

Did you design and pick out all fixtures/finishes/cabinets/tile work?

And since we are learning about construction, being able to go after work and measure cabinets for the 4th time, or compare the tile to the grout, or pick up supplies so your expensive contractor doesn't have to waste his time picking out paint colors, flooring, appliance etc... are all things that are easier to do in person.If you have a lot of experience flipping houses, or working construction,  then yes go for it, you can be successful as a long distance landlord. 

Based upon my understanding of how the dreaded "black mold" called Stachybotrys develops and the patterns it forms on surfaces, the majority of the mold depicted does not appear to be Stachybotrys.

All you can do is make your best guesses based on observable patterns and what humans usually do, and accept that even within that paradigm you're going to make mistakes. 

If your tenant wants to start paying on the 15th, he/she will have to pay the prorated rent from the 1st to the 14th and then can start paying monthly rent on the 15th to create the new rent pattern. 

You would probably not need an architect if you are just swapping cabinets, tile, floors, etc.