A private transaction is different from what is being discussed here because it doesn't involve an MLS listing at all. The issue is agents trying to play both sides by keeping ostensibly "public" listings inside the brokerage so they get both commissions, which is a practice explicitly banned by every real estate ethics body. Simply put, if you use MLS then you need to show the property to anyone who asks to see it. You can't just say "we are only going to show this to a preferred client list" or instruct the sellers to disregard offers from other agencies.