Exactly. But that implies events don't have to be occurring at the rate of a million per second.

It's not just events that drive stock prices but also investors's perceptions of the likely future impact of those events. Events which, either directly or indirectly, have an impact on a companies' value are discrete, but the assessment of the magnitude of those impacts in terms of the company's stock price takes place virtually continuously. There's no known right answer when valuing the stock price impact of some event (or the value of the stock in the first place for that matter). The subjective element of valuation (arguably the largest determinant of a stock price) means a stock will continuously be repriced as new investors make judgements about a particular event's impact, or existing investors re-assess their earlier judgements.