mac - i can't say i have inside knowledge of how Loews runs their front desks or makes assignments. However, I had always thought that hotels would service their direct bookings first before those of 3rd party (orbitz, expedia, cheaptickets) & opaque sites (hotwire/priceline/LMT). I have often wondered exactly what the OP has asked.
If you go to trip advisor and look at reviews, many of the negative comments for properties with otherwise high rankings are from those who booked non-direct and were unhappy with their room assignment.
Loews, like many other hotel chains, has their own rewards program. If you join YouFirst and attach the information to your reservation, it was my assumption it would be indicated on your reservation, along with your preferences as to room selection, etc., just as with other hoteliers. Loyalty programs are designed to reward repeat guests and I have found that written requests for specific upgrades as to floor/view/bedding type (even if they would be in another/higher booking category) are often granted automatically when the hotel is not at full occupancy.
I've utilized cheaptickets, orbitz, LMT, hotwire & priceline. The only major issue I've run into involved hotwire & priceline. All they guarantee is a run-of-the house room that will accommodate the number of guests you specify. This is not necessarily at the hotel you booked. Many properties oversell and the first people to get bumped are those booked thru a opaque site. It's not as bad as it sounds since the sold-out hotel will find you a comparable room and refund the cost of the original booking. Doubtful this is common practice at Loews or it would likely have been reported here.