Yes, this isn’t a logical error at all. If you don’t have taste in one area — actually, it’s even worse, you’re not even aware of your own lack of taste — why would I trust your taste in another area?
This is assuming that the owner is also the chef, and exclusively concerned with cooking. Being a restaurateur is a multi-disciplinary job. The owner's job is literally to have good taste in all areas of the restaurant business: food, interior design, hospitality, branding and marketing, etc. No one is saying that they have to be a graphic designer. The obvious answer here was to have the good sense to hire a local college art student for like $300 to make an endearing and meaningful logo.