Not true, either. You cannot take a bus from MK to any other park, at least not the last time we were there. You can take the monorail from MK to EPCOT. You can take a bus from EPCOT to some of the other parks. You can take a bus from both DAK & DHS to some of the other parks, also. And beware, the bus to DTD from either DAK or DHS (I cannot remember which) is a bus to DTD hotels, not DTD itself.
I never even thought about walking between EPCOT & DHS. I do enough walking around the parks each day.
I've never found the monorail to be a quick trip - usually a line to get on the monorail to go from EPCOT to MK or vice versa. We took the ferry instead one time.
If there is no park to park bus, we take a bus to the closest resort to the park we want to go to. If we want to go directly from a park to DTD, we take a bus to Port Orleans French Quarter (it's the 1st stop for the bus) and ride the boat to DTD (they reserve seats on the boats leaving PO Riverside for French Quarter and we've not had to wait for a 2nd boat if we get it at French Quarter). Just allow for plenty of time for whichever mode of transportation you use to get from park to park.
I wish Disney Transportation had park to park buses for ALL the parks. I understand why they discontinued the DTD to parks buses, but Disney, non-resort guests are using the buses to get around to other parks if they are available. So just face reality and make transportation around the World easy for ALL guests, please. I'm tired of spending 20% of my day on transportation....