I don't have any affiliation with England, or the US, and would also consider "English is a dialect of Scots". (More than one person in Galicia described the Portuguese language to me in the analogous way...).
Still, I think it's silly to go all kayfabe here and treat the languages as completely distinct. I have similar thoughts on Slovenian and Slovakian and Flemish.
People that have a vested interest in the suppression of the indigenous Goidelic language of Scotland - on both sides of the England-Scotland border - will always insist upon the full-fledged distinctive language status of Scottish English.
Unless I misunderstood your point, that is a strange take that isn't close to being true. There is a large overlap of Scottish language enthusiasts who are advocates of both Scots as a distinct language and Gaelic, the demographic of the recent surge of popularity of Gaelic on duolingo are clear.
The overlap between political commentators who both insist that Scots is "just a dialect" and that Gaelic is a dying language that we should discourage is also very apparent.
The subtext is pro indy people are generally pro Scots and Gaelic, and unionists are against both of course.
Scottish English != Scots. The former is just English with a Scottish accent; the latter is a closely related (to English) but distinct language with its own vocabulary and grammar, not dissimilar to the relationship between Norwegian and Danish, or Czech and Slovak.
Scots being a language has nothing to do with suppressing Gaelic. Generally people who hate Gaelic hate Scots equally.
The fact that you and other anglophones call the indigenous Scottish variety of Gaelic simply "Gaelic" is a pretty good example of why I continue to be very, very suspicious of those who insist upon "Scots" being a language fully distinct from English, and not a dialect - and insist upon calling it by that name.
The Irish and Scottish varieties of the Goidelic language family have far less mutual intelligibility than the English and Scottish varieties of English. Scottish English forms a pretty smooth continuum between "English with a Scottish accent", and what you'd call "Scots" or "Lallans".
But Scottish Gaelic is the tongue that gets the downgrade to "Gaelic", despite it being simply called Scottish for the vast majority of Scotland's history. Despite it literally being the reason for the country's name.
Scottish English was literally only called "Scottis" instead of "Inglis" as the Lowlanders gained a greater sense of national identity and distinctiveness from the English further south. At that point, funnily enough, the Goidelic spoken in Scotland ceased to be called "Scottis", and became "Erse" instead.
It is quite impossible to separate this insistence on distinguishing "Scots" from English, from suppressive efforts towards the indigenous Gaelic language of Scotland. You can see the exact same dynamic in Northern Ireland, where unionists play up the supposed variety of "Scots" spoken by the Ulster planters and their descendants as a fully distinctive language equal to Irish, as a means to delegitimize Irish as the primary indigenous language of the land.
I don't say all of this from a place of antipathy towards the speakers of "Scots". One need only read some Burns to see that the variety of English spoken in Scotland diverged heavily from the varieties spoken further south, and that diversity is beautiful. But the label is politically charged, and fundamentally it is a weapon - and always has been - pointed in the direction of Gaelic-speakers.
On both sides of the Irish Sea, too. Hard-line unionists in the north of Ireland have been pushing "Ulster Scots" in the last ten years or so. Not out of any real cultural association with the language or with Scotland - they overwhelmingly identify as "British" - but as a tool to diminish Irish-language initiatives. Every time there's a measure proposed to support Irish, they can propose an equal amount of funds for Ulster Scots.
It actually helps them to make the language seem as ridiculous as possible, since the real goal isn't to promote their language but to mock another.
Still, I think it's silly to go all kayfabe here and treat the languages as completely distinct. I have similar thoughts on Slovenian and Slovakian and Flemish.