You can just sit down and read Knuth from cover to cover. The problem is most people that don't get a CS degree also avoid reading Knuth on their own.
I think one of the large gaps between those groups on average is those without a CS degree think theory is useless. When you are forced to learn the theory you end up using it constantly. However, when you see a theory without the associated experience it seems useless. So it's hard to know what to study on your own. For most people it's the rigorous nature of a good CS program that forces them to put forth the associated effort.
You go to Knuth when you have already learnt the vocabulary, tho'. If you can't frame your problem in the language everyone else in your field uses, reference materials and search engines are of very limited use. You might not even be able to discuss it with your colleagues except by them basically taking over the problem and studying it from scratch themselves.
I think one of the large gaps between those groups on average is those without a CS degree think theory is useless. When you are forced to learn the theory you end up using it constantly. However, when you see a theory without the associated experience it seems useless. So it's hard to know what to study on your own. For most people it's the rigorous nature of a good CS program that forces them to put forth the associated effort.