As stated in other answers, raising your objections about public appearances on behalf of the company to whoever is organizing the interview casting should be sufficient usually. Your personal concerns are totally valid; if you do not want to appear publicly and you were not hired for it, there is nothing "logically wrong" about your objection.
I would, however, advise against bringing up certain lines of reasoning the way you have here:
There was never any mention of doing something like this at my job interview originally.
Do point out you are hired and want to work as an [insert your job], which does not normally include public appearances. But rather do not nail it down to these public appearances not being mentioned at the interview, at least not without explaining how you view this particular task as extraordinarily different from your regular work.
Realistically, job descriptions can only outline the usual activities in the job, not every one-off happening that may or may not come up at some point in the future. Thus, generally refusing absolutely anything unless it is among the tasks mentioned during the initial interview might just make you appear as unnecessarily inflexible, and in the worst case, unwilling to expand your experience.
Also, the majority of people on a similar salary to me haven't even been asked about it, so I dont see how it is fair that I have to.
This does not strike me as a surprise. Assuming you were hired for your skills in whichever job you do normally, not all of you will be equally suited to appear on film. By that, I do not mean you have to be the most handsome person in the world, just that you may look suitably "professional", your manner of speaking may be deemed appropriately suitable, like being able to form correct sentences without lots of uhs and ahs in between, and so on.
Also, note that this goes both ways. You say you do not want to see your video online after you have quit that job. Likewise, the company probably doesn't want to have an advertisement video online that contains someone who might become a vocal critic of the company later on (maybe you know you won't, but they don't). By offering this participation to you, they show at least in part they deem you sufficiently loyal to the company to represent it publicly.
Therefore, I'd bring up this fairness angle only if they really try pressing the point without leaving a way out.