<i>The second one is English grammar. In indirect speech, the tense of the speech verb normally carries over to the reported verbs, although present tense would also be permissible here, as it is still true.</i>

Aha. I didn't know that. But I probably should have, because now that I think about it, it probably works the same way in Swedish as well. If only I spent less time thinking and more time talking... ;-)