If a real estate agent is representing themselves as Buyer's Agent in the purchase of a property and credits/rebates their commission to themselves

If a real estate agent is purchasing a property, represents themselves as Buyer’s Agent, and credits/rebates their commission to themselves: would this commission rebate be considered a non-taxable event (reduction in cost basis of property) just as if they had given said commission rebate to a client that was not themselves? In other words, does the fact that the Buyer happens to also be the Buyer’s Agent make this otherwise non-taxable commission rebate taxable?

Within the context of the above, the primary question is the following: should an employing broker issue a 1099-MISC to one of their agents who represented themselves as Buyer's Agent, and credited their entire commission as Buyer's Agent to themselves as Buyer?