

It’s not pedantry, it’s using the right terminology.
And yes, self hosted means hosted by yourself. It’s in the name. https://en.wikipedia.org/wiki/Self-hosting_(web_services)
The promise of self hosting is that you own your data which may be better for privacy/security if you know what you are doing. The same doesn’t apply if you have to trust a third party, even if it is a friend/family member who provides you with a service they host. They become a service provider to you.
And what would you call your wife in this scenario? A selfhoster? Or a user of a service hosted by boonhet?
She’s not using a selfhosted service, she’s using a boonhet-hosted service. Because she has no control over the service or her data.