Although the OP's example is from casual speech, plausible deniability, seems appropriate "when someone implies something without directly saying it, so they can deny they said what they were implying".
MSN: Beijing’s ‘plausible deniability’ on arms supply is quickly becoming implausible – and could soon extend to Iran
Beijing’s ‘plausible deniability’ on arms supply is quickly becoming implausible – and could soon extend to Iran
The Diplomat: How Europe’s Preference for Plausible Deniability Shapes China’s Role in North Africa
How Europe’s Preference for Plausible Deniability Shapes China’s Role in North Africa
Yahoo: Beijing’s ‘plausible deniability’ on arms supply is quickly becoming implausible – and could soon extend to Iran
LAist: In Putin's Russia, An 'Adhocracy' Marked By Ambiguity And Plausible Deniability
Plausible is referred to an explanation, an argument, or a statement, while possible is referred to a fact, or an event. For example, my explanation on how in future time traveling will be possible could be plausible, but that doesn't mean traveling through time will be possible.
From Wikipedia fallacy - "an often plausible argument using false or invalid inference." e.g. "The fallacy of their ideas about medicine soon became apparent." "The once-common fallacy that girls just weren't any good at math." A fallacy is reasoning that comes to a conclusion without the evidence to support it.
Plausible but incorrect is distorted by illusional and by most of the other answers in this link, as there is no implication here of an attempt to deceive or be tricky, just an explanation that seems reasonable but is, or can be shown to be, incorrect. I don’t know a one-word synonym for this.