The airport owner has his 3 aircraft hangared there. Someone advised him that only immediate family could operate out of the field. I cannot find any reference to any restrictions aside from having the owner's permission.
Ask him who told him that and find out why they said that. Might be legal advice to limit his liability, might be some sort of deed restriction, might be someone who doesn't know what they're talking about. Might even be the owner just doesn't want outsiders landing there and is politely giving you a line so you'll go away without hard feelings -- be prepared for a more blunt response the next time you ask. But I've never heard of such a restriction set by state or local law.