That is true. However, because of the mounting arrangement, the full rate of the bar is compromised by motion ratios and arm lengths.
For example, the stock mopar 3/4" rear sway bar generates 167# of force. With the factory brackets,links and its applied motion ratio of .556, it produces an actual force at the wheel of 93#. A 7/8" axle hung bar generates 354# of force. With its brackets, link arrangement, and motion ratio of .366, it produces 130# of force at the wheel. So while there is a 187# difference between the bars, there is only a 38# difference at the wheels. The larger axle hung bar still applies more rate, but not as much as you would think by casual observation.
Likewise, tubular sway bars work in a similar manner. I have not done the analysis on it, but I'm betting the 1 1/4" Hotchkis sway bar has a similar rate to a 1 1/8" solid bar. So their 7/8" rear tubular bar is going to have a rate closer to a 3/4" solid bar. But like I said before, their adjustble end links allow you to add or subtract applied rate with their bar that others do not have. Plus, like othesr said, they are much, much lighter, than a solid bar so the achieve similar results with less weight penalty.