I think it depends on the video game, really, and also on what kind of criticisms or observations we're talking about here
for example, I don't really think that saying 'why does princess peach always have to be kidnapped' is somehow invalidated by whether or not you've physically pushed the button that made mario jump
no in fact I've agreed with most of if not all of your criticisms of the video - it's just that most of the people who are bringing up whether or not she "stole" her video footage are people who are looking to discredit her without actually acknowledging her opinions or the fact that there's an issue in the first place
if you really disagree with sarkeesian's videos, you need to come up with substantial and reasonable reasons to do so; coming up with some arbitrary bullshit like 'nerrr she used a let's play video instead of pushing the buttons herself and recording it happen' to denounce her series with is symptomatic of a large unwillingness to really acknowledge the issues that need to be acknowledged, here
in essence while I believe that there are probably better people out there that could be speaking about this very real issue than anita sarkeesian, I think that it's better that we have her and her videos than to go on pretending like this shit ain't a problem