Airports seem to think that the scheme is for 'Emergency landing'. It's actually for precautionary diversions.
So in my mind, your diversion would have qualified.
Having said that I think there is an onus on all of us not to abuse the scheme, and if you feel yourself that it would not be appropriate to ask for it, then you are probably right not to.
Earlier on in the year, I diverted into Liverpool when returning to Ireland, as I met a severely reduced viz as I approached the sea. On the ground, I asked if Liverpool were part of the scheme, and was told no.
Later on checking it, I realised that they were, but like you I didn't make an issue of it. I knew shortly after taking off that a diversion may be a possibility once I reached the sea......the viz wasn't great over the land.....so likely to be worse over the water, with nothing much to see.
Like you, I felt it was borderline whether I was entitled to it or not, as it wasn't entirely unpredictable, so didn't make an issue of it.
dp