There are at least four aspects to this question:
- Legal obligation
Legal obligation is a common misconception. While generally there exists an obligation not only for medical professionals but for every person to help in most (all?) countries in the world, this obligation does not work the way laymen think.
You have the obligation to help another person if, and only if:
- The other person's life is in present and immediate danger or if there is a present and immediate danger which would lead to a very serious permanent damage (such as losing a hand)
- The risk for you is "acceptable". You have for example no obligation to enter a burning building or to unfasten your seatbelts in an airplane when turbulences are likely (or even during turbulences). You have no obligation to perform CPR without mask if the person has a rather obvious "infective" look or likely suffers from contact poisoning or such, etc, etc.
You have no obligations whatsoever if the patient is merely drunk (which makes up ca. 90% of all "emergencies" that I've seen aboard an airplane during 20 years) or airsick or has a bad tummy (which are 9.9% of the remaining 10%). In fact, I have personally never seen a real emergency (one that deserves the word "emergency") aboard an airplane, but of course your mileage may vary.
Technically, aboard a foreign-company airplane, you are not legitimated to act as a medical professional most of the time. For example, the USA do not consider a German grade (although it is much better) valid, and Germany does not consider many (mostly eastern) grades valid, though the number has greatly decreased during the past few years due to EU memberships.
An airborne foreign airplane is "foreign ground", so technically you may be breaking the law by acting as medical professional even if you are normally legitimated. In practice, nobody cares, at least as long as nobody dies. The flight personnel only wants someone to take over, passengers don't know (and likely don't care at that very moment either), and medical professionals usually don't like thinking about legal stuff more than absolutely necessary (well, nurses do, but physicians usually don't).
In countries with somewhat "sane" jurisdictions, damages from administering first aid are generally covered by a commonwealth indemnity insurance. This is to ensure that people do not abstain from helping in fear of liabilities. In some other countries, you can be dragged to court for $100 million if something goes wrong.
However, medical professionals are never covered by the public insurance and are expected to have an indemnity insurance of their own (which isn't precisely free and which they must pay from their private money). Though I have never experienced this kind of problem, it is at least conceivable that the insurance company will try to perform a vanishing trick if you have "officially" operated outside your legitimation.
Reputable airlines used to give you a signed "cover everything, no matter what happens" waiver contract before you start, but some have begun to greed out based on "you need to have an insurance anyway". Which of course means that since you get no payment for a presumably disturbing work and carry the complete risk, helping gets quite unattractive.
Moral (both ways)
There is nothing special about doctors or medical professionals in general as far as moral is concerned. The same moral applies to everybody else who likes to point a finger at someone else and say "their responsibility".
Helping someone who is in danger is a moral obligation for everybody. On the other hand, getting vomited over by a stinking drunk isn't anyone's obligation.
It is, on the other hand, a serious question of morality of getting stinking only because drinks are free (not only because of the vomiting part, but also in a sense of general safety, also towards the roughly 200 other people in the cabin).