No, and nearly everyone who claims that he or she is a "strict grammarian" makes just as many errors as the rest of us.
I've absorbed the rule against split infinitives enough that they sound odd to me, but there's no reason to follow it in most situations. The same applies to ending a sentence with a preposition. Not many people care about trying to make English work like Latin any more.
Errors are one thing, but just ignoring logic in some cases is a whole other thing. And when it actually degrades language and makes it more difficult to use (such as misuse of "literally") then it's a problem.
From
Etymonline:very (adj.)
late 13c.,
verray "true, real, genuine," later "actual, sheer" (late 14c.), from Anglo-French verrai, Old French verai "true, truthful, sincere; right, just, legal," from Vulgar Latin *veracus, from Latin verax (genitive veracis) "truthful," from verus "true" (source also of Italian vero), from PIE root *were-o- "true, trustworthy" (cognates: Old English wær "a compact," Old Dutch, Old High German war, Dutch waar, German wahr "true;" Welsh gwyr, Old Irish fir "true;" Old Church Slavonic vera "faith," Russian viera "faith, belief"). Meaning "greatly, extremely" is first recorded mid-15c. Used as a pure intensive since Middle English.
Emphasis mine.