In the sense that any Chief Executive is ultimately responsible for any snafu created by the institution of which he is in charge, yes.
And, had Kerry chosen to demagogue the issue, he could have done so on this basis.
But, of course, the whole truth would be that the responsible party was none other than Her Heinous, Hillary Rodham.
By pointing out that the problem was due to a foreign made vaccine being unsafe Bush subtlely pre-empted Kerry's criticism about not allowing imported prescription drugs without ever mentioning the issue. I was surprised none of the talking heads caught that.