Or even Easyjet:
"No visible tattoos or body piercing which cannot be covered discreetly"
http://www.easyjetcareers.com/careers-in-the-air/cabin-crew-careers/recruitment-process.aspx
The truth is that a multitude of employers discriminate against people with tats if they can't be covered, or...
You're quite right, imo. But the chances are that if you have "extensive visible" tattoos, you probably won't get accepted into medical school in the first place.
Take Glasgow as an example:
"In addition, student dress must be tidy
and presentable, in keeping with patients’
expectations...