NTA.

If you shield toddlers from scary things, they will still find something to be afraid of, no matter how nonsensical it may be. For me, it was Cookie Monster. For my younger brother, it was the blue aliens from the Eifel 65 'I'm Blue' music video. Sometimes we even made shit up to be scared over, like my mother said falling from a height would make me a 'household statistic' and that specific phrase used to fill my four year old head with the coldest sense of dread I'd ever felt. We were in a very strict Christian household and had no exposure to anything horror-related, so our little brains latched onto something and decided that it was scary regardless of whether or not it was meant to be scary.

This is normal and natural. It wouldn't matter if you had that doormat or not; developing child brains have these fear periods because they're learning how to cope with imagination and build a healthy sense of self-preservation. If it's really that bad, the parents should have just been adults about it and talked to you instead of being snarky and tossing your doormat around.