Company work hours by default don’t mean everyone has to work them. They only mean company business hours, when someone can come in. Small companies usually have the most flexibility in this regard, so it’s natural for people to assume that flexible hours is a norm for non-customer facing roles. Is this a helpdesk or sales position? Is it a software developer / network admin / another technical role? Two different treatment plans.

Regarding how to deal with this or similar situation (when employee requests a non-standard accommodation), you need to try your best to accommodate them. Talk to your boss, see what you can do. If you can allow some flex in work start/end time, do so. If after all this you are absolutely sure hours are strict, you must provide a reasonable explanation why this would be the case (unless it’s obvious to everyone, like a bank teller – need to cover a specific shift). In 2017 you cannot just reject them “because I said so”.