that is correct
most "owned" floater policies either exclude coverage for "renting to others for a fee" or there is a substantial deductible (like 10k!)
if you are an owner of equipment, you must review your policy for this coverage or find out the hard way :(
having the renter provide you a certificate of insurance naming you as "loss payee" would indeed be the first policy to claim on and yes, indeed, the owners' policy would not be affected
in my many years of doing this, i have heard many many horror stories about these pitfalls for owners that rent out their gear - collecting deductibles, customers never coming back, providing fake insurance, and so forth - it can be a rough business