You are right, but this also isn't a luxury mechanic shop. A luxury mechanic shop would be a place that services and customizes Bentleys, RRs, vintage Ferraris and similar. And to your point, the clientele there will be extremely unimpressed if they are asked to speak with an AI. A place like that is as much about being pampered by staff as about the workmanship.
OP's brother is by all accounts running a successful boutique workshop, but the various luxury annotations were completely unnecessary and just detract from the actual project. If they do want to lean into the luxury segment, being cheap with AI receptionists is not the way to go. They need to hire actual staff who has experience with HNW individuals.
The blog post was written by AI. "luxury" is one of the adjectives AI likes to use a lot.