You are correct. I'm an investment broker and I have to explain this to my clients all the time.
Think about it this way... If you are looking at a calendar and you reach the ex date, it's too late. You have to purchase BEFORE the ex date to qualify for dividend. Think of the "ex date" as a big X meaning that you are EXEMPT from the dividend now.
My book of clients exceeds 2 billion dollars so you can trust my explanation is accurate