The argument is supported by the facts on the ground .
There is no evidence that can strengthen the case and until you provide anything to weaken it it makes sense to accept that assumption as the most likely .
As much as I’d like to spend time Googling the issue it’s not really for me to disprove your assertion that Bath is dedicated to a healing deity but for you to provide evidence that it is... if you get my drift :-)
If you can provide any evidence to contradict these assumptions please do . Her's a small sample url's and comments .
http://faculty.vassar.edu/jolott/clas217/projects/bath_project/Sulis_Minerva_2.htm
The Roman goddess Minerva, “as a patroness of the art of healing she was honored at thermal springs (Mac Cana 34).” This association between Minerva and the art of healing meant that she was easily integrated with the cult of the healing, water goddess Sul at Bath . The presence of votive tablets dedicated to Sulis-Minerva and sculptures of a goddess of the same name indicates that the assimilation of one goddess into the other was a thorough one.
http://sacredsites.com/europe/united_kingdom/bath.html
Dedicated to Sulis, a goddess of water, the shrine was a religious center for much of southwestern England. Soon after the arrival of the Romans in England in 43 AD, the Celtic shrine was taken over and the goddess Sulis was identified with the Roman goddess Minerva as a healing deity .
http://www.romanbaths.co.uk/walkthrough/sacred_springs.aspx
In Roman times a great Temple was built next to the Spring dedicated to the goddess Sulis Minerva, a deity with healing powers.
http://family.wikinut.com/The-Archaeology-and-Significance-of-the-Goddess-Sulis-Minerva/1w2tbl60/
Sulis-Minerva is the hybrid of the Roman goddess of healing, Minerva, and the native Celtic goddess Sul.