Yes, as you say, first appearance in print does not necessarily mean that the word was coined by the author in question. The one Elizabethan playwright who was noted (and guyed) by his contemporaries for his inveterate fondness for the coining of new words was John Marston. In one play (Jonson’s Poetaster, I believe) a character representing Marston is given a purge to force him to vomit up all his ludicrous new words, which then come tumbling out of his mouth.
Milton, a great Latinist, may well have coined many of the words that first appear in his works.
Here’s a taster of the scene from Poetaster (Crispinus is Marston):
Tib. How now, Crispinus?
Cris. O, I am sick--!
Hor. A bason, a bason, quickly; our physic works. Faint not, man.
Caes. What’s that, Horace?
Hor. Retrograde, reciprocal, and incubus, are come up.
Gal. Thanks be to Jupiter!
Hor. Well said; here’s some store.
Virg. What are they?
Hor. Glibbery, lubrical, and defunct.
Gal. O, they came up easy.
Poetaster, V, 1
BTW it’s interesting that OED gives Marston first cite for glibbery only. Other terms are much earlier, and lubrical is given to Jonson himself in Poetaster!