Of course, "is synonymous with" means "makes the same assertion about the main topic"

Indeed. "You've made more mistakes than a zebra has stripes" is therefore not synonymous with "you're in error". The former implies the latter, but the latter does not imply even the figurative sense of the former.

If what someone is actually thinking when they say "you've made more mistakes than a zebra has stripes" is no more than "you're in error", then they have used the wrong words to express their thought.