This is inaccurate. There are park-hopping buses from all parks. However, these buses don't start until about an hour after the park opens.
No, it is not inaccurate. There are no buses from DHS, ever, that go directly to the MK. They all go to the TTC...which is vastly different than the MK. You will still need to take the monorail or ferry over to the MK. Only resort buses deliver you right to the MK.
Oh, and by the way, the buses do start running about 6:30am, from resorts to parks, for early ADRs and tours.
Unfortunately, the buses from the S/D tend to suffer a bit. Any time you have the ability to get to one, or two, parks by foot, boat or monorail, the bus service to the other parks suffers. Happens to all the deluxe resorts. Buses to DHS from the Polynesian, GF and CR are nasty. It's almost easier to just go to the TTC and get the DHS bus there.
S/D share bus routes with BW at all times. Sometimes they are first on the route, sometimes BW is first. At park opening and park closing, they are the only three stops. But, in the middle of the day, you could end up on a bus that stops at the YC and then BC as well.....5 stops.
But, keep in mind the fact that the vast majority of resorts have to share a bus with others. The only resorts that don't share a route are the moderates...but they have mulitiple bus stops within each resort, so you're making multiple stops that way. Only Pop Century has a bus to itself...always.
If you are at an Epcot resort, and you want to get to the MK quickly, then you are best served by calling a cab. Otherwise, it's going to take awhile.