Yup.
That's not true la. There are tolerances built into the frame and chassis. Too stiff and more force on other components. On my Myvi it does the same thing as you reported - quieter chassis. But not on my Myvi, someone elses one, the installation on the two was somewhat forced, the cross member had to be adjusted or lifted with one of those jacks. That tells me that it was forced to fit in.
I dunno la.
With my Wira it was quite a straightforward plug and play job. Nothing was bent or shifted or moved or anything. Just take out bolt, fit in the chassis alignment kit (mine is Racetech, not Stiffring), then bolts back in (much tighter than original fitting) and that's it.
My Myvi I only fitted the two that would fit in without over coaxing the bolt in. It stiffened up the steering and made the ride harsher. Took it out after that. Wasted my money on that.