It's perfectly obvious that UNIVERSAL BACKGROUND CHECKS CAN ONLY BE ENFORCED with UNIVERSAL GUN REGISTRATION.
The absolutely only way that the BATF can be assured that any private firearms transfer has be done in accordance with any universal background check is that if the BATF knows first that the seller actually owns the gun in question. The only way the BATF can know this information is if there is universal gun registration.
Both the president and the anti-gun nuts all know this. Any statements to the contrary are lies - period.