Umm...unless they ninja changed it, the game ignores you not having the proper support or training for leve synths. I'll have to go back to the lodestone to find the post, but it was quite explicitly stated to be that way. That doesn't mean that guild facilities won't help in a general way, but if you're doing a synth for a leve and it says it requires a particular facility or specific training, it can safely be ignored.

On an unrelated (maybe) note, I have been having more issues with synthing in general lately, support or no. I've gone on runs where I don't fail a single synth for something 5 levels above me, but I can't complete something at my level to save my life. No training or facility requirements at all.