Updated July 18, 2023
No.
Along with "to insure proper service," it's a popular myth, but there are several reasons why this account of the origins of the term doesn't fly.
In the first place, acronyms are pretty much a 20th-century phenomenon, while the verb "to tip" is found as far back as the early 1600s and the practice dates back at least to Roman times, if not considerably earlier.
Secondly, you tip after the service has been delivered, while insurance is paid beforehand. So you're not insuring anything; you're rewarding services already rendered.
If that's not where the word comes from, what is the correct etymology of "tip"?
According to the Oxford English Dictionary, the word is derived from the Middle English thieves' slang word "tip," which we've seen variously described as meaning "hand it over" or "to pass from one to another," with the latter version also applying to other uses of the word, such as passing on useful or inside information (like a horse-racing tip).
In terms of the more modern usage of the word to mean a gratuity or the giving of such, that was first recorded in the 18th century.
Just to confuse you even more, another possible origin for the term is from the concept of "khiyuv" (obligation) in Judaism, whereby a seller is expected to "tip the scales" in favor of the customer rather than himself. So if you're buying a couple pounds of bananas, he might throw in an extra one for free. In Spanish, the word for a little extra is "una yapa," from which we get the word "lagniappe."
A typically Vegas word for tip is "toke," short for "token of appreciation." Other gamblers' synonyms include "juke," "duke," and "nervenzusammenbruke." (Just kidding about that last one, meaning nervous breakdown, which some people have while considering this whole subject.