I still find it surprising nevertheless. Of course the currently existing snakes cannot opt to become vegetarians now. But during the many millions of years of their evolution, some should have developed the ability to make use of certain vegetarian products.
As I said before, not so much of real green plant material like grass or leafs or such stuff. As you correctly outline in this post, that would require a very specialized digestive system fundamentally different from the normal snake.
But a option to eat for example sweet fruit, or nuts or seeds with a high fat content, would not neccessarily need such big changes in design. Also some required micro organisms could be coming from eating herbivors like mice or such. As you say - there are plenty of other reptilians who managed to make this step towards a mixed, or even solely vegetarian diet. And the advantages are obvious: fruits and nuts usually dont try to run away or bite back if you want to eat them. :)