It does basically boil down to the argument that those Indians were already under US authority to the extent that the British should have actively prevented British merchants doing business with them.So British merchants sold guns to Indian hunters they bought furs from. That's simple logic and good business. Never any sign of any government support for the Indians seeking to protect their independence from the US army. Its just that it makes an excuse for US actions against both the Indians and the British so the myth keeps getting repeated.
It's a pretty fundamental point of negotiations that not everything you ask for at some point is necessarily going to make it into the final treaty, especially if you haven't pursued a war to the point of complete occupation of the enemy state.What decades of British strategy? As Saphroneth said it was something that Britain would have favoured as it would have protected British trade in the region and also acted as a buffer against an aggressive neighbour but was never a British policy except briefly during the war when early US disasters made it a possibility. By 1814 this had passed.
More to the point, if it was a focus of decades of British strategy to establish a buffer state against the US, they'd have done it in 1782 when that was offered.