This quote from Socrates in Plato's Gorgias sums it up for me. I think it is acceptable to point out fakes in any way one desires and the owner/coveter/seller of the coin can only benefit from it. Of course, there are more palatable and gentle ways to cure someone of the evil of holding incorrect beliefs. Therefore, I understand why some people believe it should be done by Private Message only. However, if I owned a fake, I would not be fussed about the cure's method of delivery and would be happy for someone to share their knowledge publicly for both my own, and every observer's benefit.
Hypothetically, what happens if the owner of a fake, upon receipt of a Private Message, decides that they don't want this knowledge to be available to everyone else? Is the knowledgeable sender of said Private Message to throw his hands up in surrender and acquiesce to the demands of the fake coin's owner, to the detriment of everyone viewing the thread? I think not.
Therefore, it seems the Private Message is a formality done out of kindness to allow the incorrect party an opportunity to do the noble thing of their own volition, without an adversary, and maintain control over their situation and the way it is communicated.
I don't understand why anyone would get precious about it regardless. Making mistakes is a natural part of being human and no-one has completed a day, never mind a life, without error.