I find this also, though I find the FHR rates are so much worse then the regular rates that its pointless to book FHR. Having used Amex travel a few times recently, I won't be using them again:
1) It is SO hard to change a flight with them, especially once you've taken the outbound. I was on an early BA flight, when I noticed the later flight had upgrade availability. I called BA, if I'd ticketed with them they'd be able to put me on the later flight for a £100 change fee and I could have used my miles to upgrade, but wouldnt change it since it was still under TA control. I called Amex travel, and even they couldn't help me because it was done online, so they had to put me through to the 'online team' who eventually said there wasn't space in that class for them (though for BA there certainly was)
2) If you book online (which gives you the double MR points) you have to deal with the online team, who are TERRIBLE at replying to emails. I don't have a large sample, but 50% of emails aren't answered, and the rest take 4 days. Not fun when you're T-48 hours.
3) I made a flight + Car booking recently. The field wouldnt let me enter any FF numbers, and a message said book and add them later. I booked and it wasn't a problem to add the airline ones later, but Amex couldnt add it to Hertz, and Hertz also refused because it was a TA booking. I'm sure a one off, but annoying since the only reason I booked it with Amex was since I could bundle hertz with it.
Now a lot of my problems are problems that most would face with pretty much any TA vs booking direct, but I think that just highlights to me that direct is the way to go these days.