When you write "paid by the company" do you mean the company is billed for the room directly or you are using a company credit card to pay issued in your name? If you are using a company credit card then you should be getting the credit unless the company has a deal with Marriott to where they get the credit regardless. When I was traveling using an employer credit card issued in my name I received credit for each paid night.
Unless the (not a paid stay) is a reward night (using points) or other redemption (e.g. promo credit), you should get credit for the stay. Someone had to pay for the stay and whether it was you or you company, that should count toward your rewards account adding points and a night towards elite status.
When you check in to the hotel give them your Marriott Rewards number to apply to the stay. They should add it while you are checking in. If there is an issue with your marriott rewards number being added to give you credit for the night they will tell you at that time.
I have read (on this forum) of instances where a company negotiates a certain rate for a stay and no credit is given toward elite night stays.