What I read is that private sales would not require records to be kept, but the implication is that you would still be required to go to an FFL to have a background check performed.
But you cut to the real issue: If this is not doing anything harmful then why is there a bill at all? The fact they are not forthcoming on the details while making a lot of promises "we are not taking your guns", deserves a healthy dose of skepticism if not paranoia.
The politicians are ANXIOUS, DESPARATE to prove they "care" and will "do something". They demonstrate their craven need for popular accolade even at the expense of a fundamental human right, and one enshrined y our Bill of Rights. They are pathetic.
At least the NRA is stately flatly that none of these proposed bills will prevent any more crime, and they oppose them.