A tourer without a top case ????

..... Perhaps it's just that the ST is unstable under certain conditions.
I posted this "obvious" question under the parallel UK police thread but will repeat it here: Won't get Honda to admit anything, but why do you think the top-case (rear trunk) ISN'T available in the US for the ST????
http://powersports.honda.com/2010/st1300/build.aspx
...... and don't give me any "distribution problems", or "limited sales", etc. when one IS available from the factory for the VFR1200 and NT700.... " I'm just sayin'..."
http://powersports.honda.com/2010/vfr1200f/build.aspx
http://powersports.honda.com/2010/nt700v/build.aspx
Well Honda, (along with BMW, Yamaha and other manufacturers), recommend a maximum load for the top box and warn the rider no to exceed 85mph with the top box fitted.
As far as the British Police issue goes, the ST1300s used by the Police were modified. They had different top boxes loaded with radio equipment in excess of the maximum weight specified for the Hondaline top box. In addition, I think you will find that the suspension rates and spring rates were changed too to cope with the extra loading. IRRC, the Honda progressive springs were replaced by single rate springs with a higher spring rate.
I'm not saying the ST doesn't weave, I am saying that maybe it was exaggerated by the rider who tensed up and gripped the bars tighter when he/she felt what might be perceived as instability.
A motorcycle is like a giant gyroscope. If you manually introduce a sideways motion to a gyroscope, it will oscillate, leave it alone and it will always right itself. Try to stabilise it your self and it will not settle.
Hold a bicycle wheel by the spindle and spin it. Now try to turn it, it doesn't want to turn. When you do input a sideways force, see what happens. Our bikes have 2 big, heavy gyroscopes at each end and they will right themselves if you let them.
The sideways force could be aerodynamics with the airstream acting on the top box and causing the "weave", relax and let it right itself. The thing is, there are a lot of variables, from tyre pressures, suspension settings, rider weight, screen type and height, rider position, handlebar risers, load carried, it would be impossible to cover them all.
I'm not an expert, (there are plenty of those around who know better than me), but this is just my 2 cents so to speak.