No. The bottom is torsionally stiff, except for the inner bushings. The top has bushings at the outer end and stiff on the inner end. A flexing in the lower bushings gives a larger displacement at the kingpin top than a flexing in the upper bushing. Therefore the upper control arm does hold the kingpin top in place. Being weak or not, the upper arm holds the suspension.
I think the upper arm is stronger than most people give it credit for. It is forged and quite thick, though structurally taxed. The A-arm is thick mild sheet steel, but a structurally better design.
I've seen too much British engineering to give them any more credit than building extreemly cute cars. But that's exactly why I like lbc's. And also that they are easy to work on.