Yes, that is the one. But, it is not only that. The whole process of the writting the new Constitution and the ratification process was much more complicated than the simplistic comment that the Slavery clause was to satisfy the Southern slave States when in fact every State at the time was a slave State except Massachusetts, which was only a free state because on a legal technicality.
"Ratification was not guaranteed, however. The Confederation Congress might reject the Constitution, rewrite it, or refer it to a second general convention, claiming that the first had violated its limited mandate to suggest amendments to the Articles. For the same reason, the states might refuse to elect ratifying conventions. Enough state conventions might spurn the Constitution (whether as an illegitimate proposal or on its merits) to prevent its implementation. Finally, rejection by the legislatures or conventions of any or all of four key states--Massachusetts, New York, Pennsylvania, and Virginia--might cripple the Constitution, even if the necessary nine states did approve it. These possibilities dominated American politics of the time."
Of the four "Critical States" Virginia, Pennsylvania, and New York would have destroyed the new nation by dividing it in two. I fail to understand how Massachusetts would have threaten the country in such a physical manner.
The fact is that the political manuvering between all these States for position as to who was going to be the "big dog" at the table was terrible. As the old saying goes, 'if you want to know who was pulling the strings Follow the Money'. If you follow the money it will lead you to New York and New York Harbor, the #1 import and export harbor at the time and even today. It wasn't the Southern States that needed the Slaves the most. It was the New York Harbor masters. And if I remember correctly the date of New Yorks ratification of the Constitution was AFTER the Constitution had been ratified by the 9 required States and the old Articles of Confederation had been abolished.
Look at what New York got when it did ratify the Constitution. It was made the Capital of the New United States along with the banking interest and other governmental interests and functions. Were those a payoff? So why it is so far fetched to think that the Slave Clause may have been placed in the Constitution to intice New York to Ratify that Constitution