This source indicates that vitamin k uptake is very poorly understood, but that vitamin k deficiency is rare in practice and that you have to put people on a very low vitamin k diet for an extended period to show any negative effect at all. This would be very weird except that our gut flora is known to produce vitamin k, so we're probably producing a fair chunk of what we need internally.

From that article:

It is commonly held that animals and humans obtain a significant fraction of their vitamin K requirement from direct absorption of menaquinones produced by microfloral synthesis (43), but hard experimental evidence documenting the site and extent of any absorption is singularly lacking (18, 19, 23).

Based on that article there's certainly grounds for adding some green salad to that sandwich to be on the safe side, but it seems likely that your gut flora would keep you going regardless.

I was pretty sure that vitamin k deficiency was practically unknown (and a vitamin k overdose relatively dangerous), and so for that reason making vitamin k supplements available was generally seen as a bad idea, but I learned a bit more about the whys of that because you raised that question, so thank you.