1) We know sedentary hunter-gatherers existed throughout the upper paleolithic. This is a bit of an under-researched area for various reasons, but we know they definitely weren't all mobile.
2) Humans had been continuously inhabiting areas in east Africa since even before they could be called anatomically modern. Yet, agriculture there emerged at roughly the same time as elsewhere.
3) The earliest agriculturists were semi-sedentary anyway, not predominantly sedentary and fixed in place. How mobile they were depends on where and when we're specifically talking about, as it varied over time.
4) Climatic variability in New Guinea (another early center of agriculture) actually increased during/after the younger dryas.
This one's a bit unfair, as it's outside the scope of what I originally said. Nonetheless, it'd be nice if we could also use our explanation to say things about independent domestications long after the start of the holocene, like the eastern agricultural complex.