Unless you research every business's shareholder lists and company history you almost certainly do business with several such family owned concerns. There are a plethora of familiar high street names, whose premises are run as franchises, and the people you see face to face are actually employed by a private and often family owned business.
However I do agree with the notion that being "family owned" is not a guarantee of better service or value, but it's rather like a common description used for butchers and bakers where their shop sign includes the words "High class"
It harks back to earlier time's when family run businesses needed to build a good reputation in their community or face being shunned.