I've always heard "jive" in this context. It means it doesn't fit the situation or doesn't or can't be true in a particular. For example, eating donuts & smoking cigarettes doesn't "jive" with someone's intentions to stay fit & healthy.

That.s a old word that's hardly used anymore. It basically means that does not make any sense. Like the cow jumped over the moon.To some this does make sense I guess.

According to an online dictionary, the word JIVE dates from the 1920s in the US, and originally signified meaningless or misleading speech. Then in the 40's and 50's, jive was used for a swing type of popular dance.

The way I have understood the phrase "that doesn't jive," is to mean incompatible, it does not fit in with the truth; such as,
"What the politician is telling us does not jive with the facts."

A jibe, by contrast, means to make insulting or mocking remarks or jeer. The example given in the dictionary is "Some cynics in the media might gibe."

Wrong.
The phrase does not have a ghetto or slang origin--it is not jive, it is JIBE.
The correct phrase has a nautical origin.
Example: "Your opinion doesn't JIBE with the facts."
Its origin is nautical predating the 1800s. To jibe is a method of coordinating the sails on a boat when turning or when the wind direction changes.
To JIBE is to COORDINATE.
To NOT JIBE is to lack coordination, to conflict, to not make sense.