Does Deflationism Rule Out Relativism?

Bill thinks so.  He summarises:

No deflationary theory of truth is a substantive theory of truth.  All relativistic theories are substantive theories.  Ergo, no deflationary theory of truth is a relativistic theory of truth.

Yet it seems to me that to arrive at this dichotomy both the deflationist and the relativist have 'factored out' the most significant relativistic aspect of all this.  Namely that the truth of 'snow is white', 'grass is green', and the rest, is relative to, or at least dependent upon, the existence of speakers of English.  This becomes obvious if we render

'Snow is white' is true

not as the bald

Snow is white

but as

The stuff we English speakers call 'snow' is the colour we call 'white'.

It's as if the deflationist, having forgotten this, is happy with an empty theory of truth.  The relativist has also forgotten this but isn't happy with the result, and scouts around for an idea to fill the vacant space.

Perhaps another way of putting this is to say that if we are looking for a truthmaker for 'snow is white', then we need to look beyond snow and beyond white and include, as part of what makes 'snow is white' true, we English speakers ourselves.

Again, Bill says,

One version of deflationism is Quine's disquotationalism according to which the function of the truth-predicate is to remove the quotation marks from a quoted sentence. Thus "'Snow is white' is true" says exactly what 'Snow is white' says, namely, that snow is white. And "'Grass is green' is true" says exactly what 'Grass is green' says, namely, that grass is green. And so on. There is nothing common to these sentences in virtue of which they are true. 'True' is just a device of disquotation; it does not pick out a genuine property.

But we can render these sentences as

The stuff we English speakers call 'snow' is the colour we call 'white',
The stuff we English speakers call 'grass' is the colour we call 'green',

and it's apparent that these sentences have a common form in which the correct word for a certain colour property and the correct name for a certain stuff are used to assert that the stuff has that property, and it does. Is this irrelevant? Naive correspondence?