It seems pretty established that 10/300 was on the table. They had to have known that he wasn't going to take it at that point. You don't risk injury and all that to go that close to free agency and then take the offer from your team, especially if you are repped by Boras.
So, the motivation was either 1) a token offer to appease the fans, or 2) it was offered like "Here's our offer, go shop around and see what's out there. We'll keep the offer open, if you agree to let us try to match any better offers.". Or another option was that 3)they thought they were making an aggressive offer, and said take it or leave it up to the start of free agency. The second option seems most likely to me, followed by the first, and the 3rd option just doesn't seem consistent with how the Lerners have treated Harper.