If you lease a car for two years from any car company, you would still say it's "my" car. You wouldn't go around telling people "no that's not my car, it actually belongs to X company, I'm just leasing it." Of course you wouldn't, that would be ridiculous! But apparently the FAA has a very different set of rules. Case in point, the US Department of Transportation recently fined a non-profit air ambulance company (Mercy Flights of Medford, Oregon) $30,000 for saying that the helicopter they are leasing is "ours". You can read the details here.
Thank goodness our government has the time and money to keep such blatant violations under control!