Can't restore tile in lower level

[Karen O.]

I'm working on a split level reno in MA.  

The lower level has a room with a porcelain tile floor I thought could be restored with a good cleaning as it is in good shape.  Company came out, tested and declared it could be "cleaned and sanitized" but the stains, which might be rusty water or pet urine, can't be removed.  As there is no smell, I'm inclined to believe it's rusty water.  

It's about 350 sf of tile installed over concrete.  Removing/replacing isn't a cost I want to incur.  Would I be on the right track if instead I sanitize and install vinyl file over underlayment? 

Appreciate any and all thoughts.