With the right machinery, you can make silver gelatin prints with little or no "hand" work.
I know guys who work in digital that put every bit of effort into their digital prints that I do with any darkroom print, and their results show it.
And as pointed out, it's not a matter of just hitting a "print" button.
Further, even with silver gelatin, should you want to make multiples using only analog methods, it's perfectly possible to create an ideal print, make a film copy of it, then make identical prints with no further burning, dodging or other manipulations. Doing that may be somewhat more work than doing it in PS, but the choice is available.
What really matters is the print, and a discerning viewer will appreciate the work that went into it regardless of the method of work. For the others "hand printed" I wager that won't have any meaning to them anyway, though education is always a possibility.
It may be sad that the term gets misused, or is not appreciated, but I don't know that it deserves to be sacred, or reserved for anlog work.