I think it's quite OK to say "really" instead of "very" -- certainly in informal contexts: "We had a really good time last night."
In fact, one could argue that "really" in that sentence is not an informal substitute for "very," but a legitimate standard adverb in its own right, meaning "genuinely" or "truly."
It is "real" rather than "really" or "very," used in place of "very," that I said in 18 I would describe as non-standard. (Note that I said "non-standard," not "substandard" -- but come to think of it ...)
As for "regional," I was speaking of regions of the US, as I live in the US and AE is what I speak. I think that in some regions of the US, the "real" we're considering would be used mainly by the un(der)educated. In other regions (for example, the Ozarks) it might be accepted even among the local elites.
(For what it's worth, there is a number in the Rodgers and Hammerstein musical Carousel called "We had a real nice clambake." That musical is set in Maine, not the Ozarks or Texas. On the other hand, the characters are traveling carnies, not doctoral candidates.)
The citation from MW notwithstanding, I think it would be a mistake to advise a learner of English to mimic such usage as "The water is real warm."
By the way, I don't quite understand this sentence from the citation:
It [real] is used as an intensifier only and is not interchangeable with really except in that use.
That means the author thinks that real and really are interchangeable in the case under consideration, right?
If so, my recommendation is to go with really.