I booked last week.
Prior to this I posted a similar thread and there were several positive responses.
Haven't stayed yet so I can't comment any further. However, I called the hotel and confirmed I was in their reservation system. It's like booking through any third party such as Expedia.
If you want 100% peace of mind then book through Loews directly.
UT has been around for a long time though and I got an excellent rate so I used them.