'Perhaps a few videos of cars RLJing would redress the balance.'
'I get the impression they feel they are redressing the balance'
Pretty much this. If it's acceptable to film bad driving and post it up for all to see/mock/discuss you can't reasonably justify the same not applying to cycling. Any arguments about making the majority of law abiding cyclists look bad also apply to drivers all the same - so do any discussions about how many drivers are law abiding. I do poke around motoring forums now and again (know your 'enemy' etc) and it's inevitable that someone will post a dashcam video of a cyclist RLJing, which for some folk is going to be just one more bit of evidence about the feckless lawless scum we are, but for the majority it's just another video of one particular persons bad cycling and shouldn't be made to mean anything more. Of course I've seen a fair few videos purporting to show dangerous cycling that come down to a cyclist being very naughty by riding in the primary, being assertive, not wearing a h***** or hiviz etc, but the type of person who gets outraged by that probably isn't liable to being easily talked out of that mindset anyway.
If you spend some time looking around for these videos you see everything. Dashcams showing good driving, bad driving, good cycling, bad cycling, helmetcams (both bike and motorbike) showing good driving, bad driving, good cycling, bad cycling, etc. Doubtless there's a few desperate to maintain the WAR ON THE ROADS!!! stance but they really are not the majority.
Myself, I have no qualms about being filmed, as I believe I ride safely and would not be seen doing otherwise.