Secondly (1), if both sides really did put up a stake, the ḥadith is actually evidence against you (2), for he said, “Shoot, for I am with the clan of So-and-so,” while a muḥallil never aligns himself with either of the two teams.
Thirdly (3), if the stake was offered by only one side—or if no stake was offered at all—your appeal to this ḥadith collapses. Either it stands as a proof against you, or you have no proof in it whatsoever.
If it is asked, “What, then, was the point of the Prophet ﷺ joining both teams if he was not acting as a muḥallil?”—
The reply is this: when the Prophet ﷺ first sided with one party, the other party held back, for they knew that whenever the Prophet ﷺ was with a faction, that faction would be the victorious and supported one. They therefore did not wish (4) to be in the party that lacked the Messenger of Allah ﷺ. When he perceived this from them, he put their minds at ease and said, “I am with all of you.”
This is the purport and indication of the ḥadith; it is wholly innocent of any notion of taḥlīl. Success is granted by Allah Most High.