The case
It's etched on the mirror of every car you learned to drive in, and the mind still softens it. The regulation text is definite: the objects ARE closer, because a convex mirror shrinks them.
Two '90s hits nudged the memory. Meat Loaf's 1993 song "Objects in the Rear View Mirror May Appear Closer Than They Are" put the hedge into a title, and Jurassic Park's T. rex chase gave the mirror its most famous close-up.
Why our brains do this
A hedged version appeared in pop culture, and hedged language feels more natural than a flat statement.
Sources: Wikipedia — Objects in mirror are closer than they appear · Wikipedia — False memory: the Mandela effect