These days there is little chance for CS from anywhere if not directly admitted, for reasons explained above. They have over-enrolled for years.
However, in general, there is a difference between being offered DGS and wait list, at least in some cases. The school is a little dodgy on giving out details, which is why I suggested you call.
Here is a thought experiment…
If May rolls around and yield is lower than expected in a given highly-selective department, where would you go to fill spots? By going to DGS, you are taking students (presumably the most qualified) who have already agreed to attend and pay tuition and just moving them over to a different department. University-wide you are still under-enrolled! You now have to go out and fill those newly-empty spots in DGS.
As someone on the wait list, how interested will you be to help them fill one of those newly-empty DGS spots, considering you are a first choice ENG/BUS applicant? Not very interested, especially if you were only borderline rejected from that first choice, as you will have many other great college options. It will be the same for anyone in your shoes, and the school will likely have to lower its standards to fill those DGS spots.
Now if you are the school, how do you maximize the number of very strong students enrolled? Simple, you keep those strong students in DGS, who have already agreed to enroll, and use the wait list to fill the empty spots in the highly-selective department directly. There is no need to lower your standards to fill empty spots in DGS, because you are admitting directly to a very popular major and will be able to attract the best students off the wait list.
This is why I think that, in some cases, students offered a spot on the wait list are in a better position than those offered a spot in DGS. I reserve the right to be completely wrong.
PS
@CSmajorQ apologies for the snark