Well I guess the time scale is what determines the degree to which the distinction becomes opposition. AI is likely to persist for tens or hundreds of thousands of years in some form. Are any of today's nation states built to last that long? I think we all know the answer.
If you have AI which is in the service of an entity which proclaims itself to be the sole franchise of government authority over a given landmass, it is strictly incorrect to say that this AI is "for the country", because it's perfectly plausible (and on sufficiently long time scales, inevitable) that the country will want to evolve, replace, or deprecate that entity.
I agree that “AI for governments” is much more accurate, just saying that diametrically opposed doesn’t really capture the relationship between the two concepts well