They don't, as far as I've seen for windows PCs. I've tested different drivers and OSes with my capture card and not found any difference in dithering for the same cards. The only time I have observed changes to the dithering algorithm were when switching between different colour formats on graphics cards that support it.
I don't doubt people's experiences, but any allegations that it is due to a change in the dithering algorithm are completely without evidence. Many times I have investigated my own visual discomfort expecting to find dithering to be the cause, only to find otherwise after testing.