Should it be up to the parks to educate the public? Yes it should - it is their product being 'tarnished' and they are the ones that stand to lose big if this misinformation campaign continues.
Here's a few things they should consider:
Have a protocol set in stone that is enacted every. single. time. a ride goes into fault \ e-stop. Operator to spiel using microphone or other method to all guests a short explanation - if it's guest safety related - ie: standing up on the ride \ holding loose object like a phone - then say so "guys we've had to stop the ride because someone is <reason>. We'll have you back underway shortly. If it's ride system related, then as someone said above "guys, the computer system isn't happy with something, we're going to bring you back down and quickly reset the ride - it won't be long".
(The thing about Disney is the automated spiel usually isn't specific - eg: Haunted Mansion "Playful spooks have interrupted our tour. Please remain seated in your doom buggy. We will proceed in just a moment. We have been unavoidably detained by pranky spirits. kindly remain seated in your doom buggy please, we will continue our tour momentarily" Which works fine when the operator isn't sure what the cause of the stoppage is (or in the case of haunted mansion - when they're loading a mobility assisted guest)
Continuing with the stoppage protocol, if the ride operator isn't able to resolve the issue within a minute (i've seen them restart Tail-Spin 4-5 times without calling for maintenance) then that's really all thats needed - but if you're going to call for assistance - maintenance, security, management etc - then there should be a 'kit' containing vouchers for freebies - a bottle of water, a snack, a meal, a free return pass - put them all in the kit and let the supervising manager on duty decide what is necessary. In that kit it would be helpful for them to have umbrellas to shade stuck riders from sun or rain (where possible). First Aid \ Park Nurse should also be despatched to provide reassurance to anyone feeling ill effects afterwards.
Operator should continue to spiel at each step advising what is happening: "guys we can't get the ride restarted so we've called for a technician to come and reset the ride - won't be long" - and this should be done every couple of minutes - for a person stuck up high on a ride, a minute can seem like an hour - however the announcement shouldn't be scripted - it should always provide new information - nothing is more infuriating than someone telling you 'won't be long' repeatedly for 20 minutes.
Supervising manager, or whomever is the 'senior' person on the ground when guests are released should meet the guests - in a group near the exit, or individually if it takes a few minutes to release each row, and explain in simple terms what happened, what went wrong, why they were never in any danger etc. They should offer an apology, offer the services of the nurse if anyone isn't feeling well, offer some sort of freebie, even if it is just water.
Finally, they should provide them with a card that gives them feedback options - phone, email etc. This shouldn't be the generic info line - it should be exclusive to people who have been in this situation, and it should be responded to religiously and without delay. The card should have a 'reference number' or similar written on it, that corresponds with an 'event book' used to record these events. A staff member during the incident should be recording the event with as much detail as possible - ie: '10:47 - ride stoppage on Giant Drop - requested maintenance, security and manager.... 10:55 - all staff on scene. 10:56 - operator spieled to riders about delay 10:57 - maintenance restarted ride 10:59 - all guests evacuated safely. Having someone note each and every detail as it happens helps ensure that details aren't missed, and also helps to refute the claims of riders on facebook who come on and say 'we were up there for an hour and they told us nothing!'
"safety videos" as mentioned above are another great idea. Not sure where you'd play them - but perhaps sharing them on social media would help combat the misinformation. you could do general videos for most flats and specific ones for more complex attractions. there are plenty of folk out there today capable of putting together a quick 30-120 second video covering the basics - "green lantern has XX sensors throughout the ride, each pair provides the same information to the computer. if one provides different information to the other then XXXX happens" "xx ride has a failsafe 'deadman' switch that requires the operator to hold it down to operate" "if the air pressure to operate the brakes is lost, all the brakes will close" "your harness \ restraint is secured by XX. it also has YY and ZZ to ensure it cannot be opened whilst the ride is in motion"
I have worked for an organisation that in the past had a policy of not responding to baseless media articles. It frustrated us as staff that they wouldn't refute claims made by the media. After a change in management, they changed their policy and now actively refute false claims in the media - it has done alot for staff morale, and has also improved customer perceptions of what we do. Media outlets are required to contact the subject of their article to advise of the claims made and offer them an opportunity to provide a response - if the park responds, the media must provide that response - that's why you see so many articles saying 'media outlet has contacted XX for comment, and at time of publishing, no response was received' - but they should stick to issuing statements to the media for all but the most serious of events, and not put their staff \ spokesperson in front of camera for random questioning.
This was a good read:
http://www.wdwinfo.com/walt-disney-world/why-rides-stop-at-walt-disney-world/
...and while this isn't directly related, it's on a similar-enough tangent that i came across whilst googling so i decided to share it too:
http://www.themeparkinsider.com/flume/201008/2049/