I have seen this nonstandard spelling more than once:
But investigators say Furey had actually been showing the boy the gun when it accidently discharged.
To teach someone how to avoid this spelling, I would remind him or her that the shooting could be described with the adjective accidental. So when we use the adverb form, we add -ly to accidental. This is advice derived from Paul Brians’ explanation.
A variation of this reasoning helps me remember how to spell publicly and avoid the error publically. The adjective is public, not publical.
Of course, someone will counter with the argument that accidently is a standard variation, found in dictionaries. That spelling may be fine in informal writing and Microsoft Word’s spelling checker doesn’t flag it, but the irreproachable form is accidentally.
It is a copy editor’s job to enforce standard spelling, the forms that will pass unnoticed by the most discerning reader. That’s why copy editors need to know the shortcomings of computer spell-checking programs and to catch the tricksters that sneak by.