A word for a statement that sounds true because it sounds good
Solution 1:
Verisimilitude means "the quality of sounding true." So if you wanted to be very pretentious and formal about it you could say something like "verisimilitude by euphony."
(This example was recursive. :) )
Solution 2:
The newish word "truthiness" sort of applies here but focuses more on gut feelings or things that just seem true instead of a statement's visual or oral attractiveness.
Solution 3:
The word you're looking for is specious.