Is the thumb a finger? The medical danger of numbering digits

Is the thumb a finger? How many fingers does a person have on one hand? Difficult questions? People have had the wrong finger(s) amputated because some health care workers refer to the digits of the hand by number e.g. first finger, second finger, etc and this can be confusing. Would it not be safer and simpler to refer to digits by thumb, index, middle, ring and little fingers?

This debate has been going on for at least 60 years. See these three papers:

Forbes R. Numbering fingers. BMJ. 1955.
 Addison PH. Operating on the Wrong Limb or Digit. BMJ. 1960.
Masukume G. Pointing fingers. CMAJ. 2009.

While this debate has been raging, in this digital age, wrong digits have been lost.

Bonus: There are at least 27 finger counting methods.