Except the book just says those are the most common, not the only.
Tell him he's a f@#$ing dingus and he should learn to read better if he's going to try and be the douchey sort of rules lawyer.
Heal: makes you a healer.
Profession: healer, or doctor, or travelling Chirgeon, or whatever, makes you proficient at the nuts and bolts of getting paid to use the heal skill.
things like sourcing clients, setting up shop, and knowing what licenses a town may need you to have. drumming up business, keeping the books and paying the appropriate taxes.
It is possible to be a healer (heal skill) and still try to make a living (untrained wisdom check) it just makes you a good healer, but a terrible businessman
It is possible to be a healer (profession skill) and still try to heal others. but you will be untrained. BUT you will know all about the business side of the job.
Both is best
If you're an Aasimar the Faith Healer trait lets you maje Heak checks for cash by the by.
The usual example I use is Profession (baker). Profession (baker) is the skill that makes you a successful _professional_ baker.
I'm sure we're all familiar with at least one person who is a fantastic cook (or baker) but who couldn't actually manage to serve the public on a day-to-day basis.
As the movie Ratatouille put it:
You waste energy and time! You think cooking is a cute job, eh? Like Mommy in the kitchen? Well, Mommy never had to face the dinner rush while the orders come flooding in, and every dish is different and none are simple, and all different cooking time, but must arrive at the customer’s table at exactly the same time, hot and perfect! Every second counts and you CANNOT be MOMMY!
And, yes, the other way works as well; it's possible to run a successful restaurant without being a very good cook, or a successful bakery without being a very good baker.
So what do you call someone with Profession (doctor) but no Heal skill? A quack with a good bedside manner. Conversely, if you've got someone with the Heal skill but no Profession (doctor), you've probably got a low-paid version of Gregory House, because he can't handle the running-the-business aspects of working in and with the rest of the organization.
Best question:
'What will I roll when I want to run a business as a doctor?'
If the GM decides that Heal covers the business side as well? Eh, why not? Decent enough interpretation, and I can understand a desire to not want to be too granular on skill points. No significant harm done -- if you're serious about using it as a professional-style skill, your skill points will make up for a lacking attribute.
Otherwise, that's pretty much where things end up going downhill. Your question is effectively 'What skill is the local doctor using for his practice?'. The game seems to assume that the running-business side of things is subsumed into the actually-doing-it side, as Craft checks can be used for jobbing (or Performance (pro wrestling) for the other jobbing). I can understand wanting to show some love to Profession, which seems to have even less love than Craft does, but if the game's main concern is 'can you do the job itself?' when it comes to pay day, that's how it's set.
i always thought that to have a profession you had to have the skill to do it. like craft weapons and armor -> blacksmith-> weapons shop merchant. craft alchemy -> herbalist?/heal-> aprocrothist's/potion shop merchant(i know its spelled wrong but i just cant get the right word out of spell check like a medieval pharmacy but for magical remedies).
Apothecary
Being a Doctor does not mean you can do everything on the Heal skill list. Nor are you limited to that list. Is treating psychosomatic ills something a Heal check can do? No. Is teaching good sanitation on the list? No. Is managing a couple of Healers on the list? No.
Doctor is a fine profession.
Doctor is a learned professional, not necessarily of the healing skills. Doctors can be scientists also. Are you an Astrologer? That is a profession where you can be called a Doctor. Are you a Time Lord? Another one.
/cevah
Given that various professions stand in as the relevant skills under certain circumstances - such as Profession(sailor) when operating a ship, or Profession(siege engineer) being on par with K(engineering) for qualifying for siege combat feats - I'd say a Profession skill actually does give you the tools of the trade. The Doctor without Heal skill relies on his shop and his tools, and cannot do a Heal check under pressure, but Profession(physician/surgeon) gives him some medical training as well as covering marketing.
I generally rule it that someone with Profession skills has all the relevant trained skills to their profession under ideal circumstances... say Profession (trapper), can make Disable Device checks related to disarming an animal snare and Survival checks to forage for food in the wild on their P(trapper), but not general Disable Device and Survival checks.
Adding Profession(physician) or Profession(surgeon) to the list seems perfectly fair - Profession(midwife) and Profession(herbalist) are already there as particular medical professions.