Perhaps mistakenly, I've based this answer on the assumption that you are asking for a term that is the converse of sniglet. Also, I assume that by should not exist [in dictionaries], you intend that the word should not be in dictionaries because of objective, evidentiary reasons, rather than because of subjective, emotional reasons. So, I'll provide
a word/short-phrase for a word that does exist [in dictionaries], but shouldn't [because it's not a word].
The term for "a word that does exist [in the dictionary] but shouldn't" is 'spurious', or 'spurious word'. I was fascinated to discover a list of these apparent contradictions in my free 1970s book club OED-with-magnifier.
The terms, 'spurious' and 'spurious word', satisfy your examples:
He referred to the man by a term so vile, the word itself should be spurious.
After six hours of listening to corporate double-speak, he came to regard every buzzword as a spurious word, invented simply to annoy him.
The first 'spurious word' currently provided in OED Online is
This explanation is provided in place of a definition:
Prob. a misprint for baton n., to which the word is emended in many modern editions of King Lear. The Quartos read battero (which is prob. another spurious word, perh. arising from a wrong expansion of a typographical abbreviation of batton, variant of baton n.) and bat bat n.2 The word is given in later dicts. (e.g. Bailey (ed. 3, 1726) and Grose (1787)), based on the occurrence in the quot., but does not appear to be attested independently. For an alternative etymology, see E. Ekwall in Eng. Studies (1941) 23 99–101.
["ballow, n.1". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/15006?rskey=GkvnKr&result=1&isAdvanced=true (accessed January 09, 2016).]
About thirty other 'spurious' or 'probably spurious' words are provided by OED Online. They include such delicacies as
Spurious word in Ash, etc.: see disgorge v. 3.
a spurious word in Dicts; see evocate v.
A spurious word found in some heraldic and other Dicts. in the phrase cross enhendee (given as synonym of cross potenee) where the adj. appears to be a corruption of Old French enheudée having a handle. The misreading occurs in French writers, e.g. Palliot, 1664.
Spurious word in mod. Dictionaries: see fruticulose adj.