Bath tub is corroded and somewhat pain to use in that type of set up. 

The liner in the bathtub... so grossthis is on the ceiling..

@Mike Bryant - Lowes sells a kit for painting bathtubs and tile that I've used in the past.

But my car fits a bathtub (no joke) and a 6 foot ladder in it and pretty much anything I want from home depot.  

If the home only had one pipe that ran to one faucet it would do what you believe it's doing in protecting the water line from freezing, but homes have multiple water destinations, kitchen sink, dishwasher, ice maker, bathtub, vanity faucet, showers, toilets etc...with multiple water line branches.That system works only as a localized system on the trunk line or water line that is in direct line from the place you have it installed, back to the water heater, there are other water lines that branch off from the water heater at some point and odds are greatly not in your favor that you're pulling the water from those lines and recirculating it.  

Speaking with the inspection company the growth is in areas that could have been the tenant being careless. ie: water from shower and bathtub.

Upstairs shower had a bad (Horrible) connection on the pipe leading from the bathtub to the shower head.

The bathtub draining pipe was also not connected water just run out beneath the house.

Plumbing issue resolved for about $300 including the microban to clean up the inside mess.My Mom recently had a septic tank issue and the lines were backing up into her terrace bath tub.  

If you just wanted to change the color, then you could have probably had someone reglaze the existing tile in black, just like they do with bathtubs.