Yes, I would have taken the letter to mean that John was the son of Henry of Faskally. Indeed all the evidence suggests this. The natural conclusion from this is that it was John Scott Butter. This is only contradicted by the fact that he died at Bath in 1800. This fact is taken from "The Gentleman's Magazine, Mar. 1800, p. 288"
"At Bath, John Scott Butter Esq., second son of Henry B. of Faskally and late in the East India Company's service"
So, as you say, then there must be another explanation. I think you're right in suggesting an illegitimate child. Henry did not marry Katherine Hay until 1767. Henry was working in the western Highlands since the early 1750s, so an illegitimate child may have been born during that time. However as any record is likely to be under the mother's name, I'm not holding much chance of locating one.
I can find no record of a will for Henry, as far as I can tell, so no clues there; his wife Katherine died intestate in 1813 so, while there is a testament dative, it is unlikely to mention beneficiaries.
The other option is that there were wider family living at Faskally with Henry and that John was a son of one of those.
I will pursue the fact that he was in Edinburgh in 1803. If he was resident, rather than just passing through, he may appear in the Edinburgh Directories. When time permits, I'll be consulting the Clanranald papers as well.