Best I can recall, over the past 6 years there have been a number (10? 15?) of people who have posted first hand experience with their bikes bouncing a lot, who on testing their 1-1/4" receiver hitches found they seemed very flimsy.
I haven't kept count, but I think several people actually reported that they personally lost bikes from these hitches. I put more weight on first hand experiences than on stories about other people.
So there's a prevailing opinion that the 1-1/4" receiver hitch is not strong enough to carry bikes.
As with many issues, a relatively small number of problems can be magnified by the number of posts discussing a few failures.
That all said, bikes on bike racks do bounce and put a lot of stress on any receiver hitch. The 1-1/2" receiver hitch just isn't very strong. Some have failed and bikes have been lost.
And at least one owner's 2" custom receiver hitch has failed and the bikes were almost lost. There's a lot of stress.
I have a 1-1/2" and have not yet lost my bikes, but I also have them tied up to the ladder with bungee cords to minimize movement. And I'm thinking about moving to a 2" receiver.
So, you pay your money and you take your chances.