Define a "few weeks." Two, three, four?
If you can't get your renewal bound a "few weeks" before expiration, then you are stuck with the short term insurance cards with the upcoming expiration date.
As to what the dealer wants, he can want whatever he wants and if you aren't able to give it to him, walk away from the deal.
When his money is walking out the door he will suddenly find that the short term insurance card is acceptable.
Besides, it's not the dealer that is of concern, it's what the lender wants. If you can't satisfy the dealer's lender, find a lender that will accept the short term insurance card.
Or delay the purchase until after your insurance renews and you can get the card with the full policy period.
If you have already made the deal and swapped vehicles, read your purchase and loan contract and see if it says you have to have at least 45 days on the insurance cards. I doubt if you'll find anything like that in there.
As for the title of the thread - car dealers never tell the truth. They are liars and thieves.