I think you're mostly right, except that the definition of species comes from does breed with, rather than could. Also, in your example, your ancestor of 10 ge

I think you're mostly right, except that the definition of species comes from does breed with, rather than could. Also, in your example, your ancestor of 10 generations ago cannot breed with one of his contemporaries but 10 years junior, because they're both dead. This isn't hair-splitting, it provides the practical answer to your question. There's no potential for mingling genetic material between those two organisms today.