...something correct, agreeable, or even tautological
A thought-terminating cliché, you mean?
When a commonly heard and accepted phrase is rhetorically introduced as a substitute for an actual argument. (logfall.wordpress.com)
From Wikipedia's List of Fallacies:
Thought-terminating cliché – a commonly used phrase, sometimes passing as folk wisdom, used to quell cognitive dissonance, conceal lack of thought-entertainment, move on to other topics etc. but in any case, end the debate with a cliche—not a point.
Examples from Logfall:
The phrase “Only God knows” is often interjected at the end of a discussion to imply that no one is justified in taking a position on the issue, or to assume the evidence is balanced on both sides.
Sometime the phrase “Freedom is not free” is used to justify initiating or entering a war.
Christians often quote the verse “The fool has said in his heart, ‘there is no God’” sometimes as if this is a justification for belief in God, and sometimes simply as a thought-terminator.
When having their expectations questioned, older people often, due to either having no real answer or having no interest in giving an answer, say “When you’re my age, you’ll understand.”