I don’t know if that’s true. I see tons of car repair services advertising “we repair $BRAND with original parts” and they’re definitely not owned by $BRAND.

Clearly not confused with the original brand, but also advertising a service built off that brand.

Right, but they aren't naming their business "Bob's $BRAND" which is kinda the point.

How can that be the point? That would be parallel to Amazon calling itself Elasticsearch, which never happened or was even a remote possibility.

The parallel is Amazon called their offering Amazon Elasticsearch Service.