I've talked to owners of both sizes of V-strom and they report their bikes as "really top-heavy". I'm supposing that with a bike that narrow and that tall, their conlclusions are pretty fair.
Let's face it, all bikes will seek "horizontal", if not, the sidestand wouldn't work. They, like bicycles, balance much better at speed. Much of the problem with the "top-heavy" feel has as much to do with rider awareness/skill as anything else. I have laid mine over and it was a "stoopid rider" trick. Once a bike of this size gets "out-of-shape" it is really difficult to recover. It is a 600+ lb. motorcycle that, when is allowed to get 20-25 degrees leaned over at a stop, is going to be most difficult to hold up.
That being said, if one pays attention to the things that can cause an upset: sloped street/shoulder, soft gravel or sand, turning the front wheel to sharp on a sloped surface, there shouldn't be a problem.
IIRC, most of the stories about drops are based on the rider making a critical mistake when assessing the terrain/road surface they were approaching. I've seen Goldwings and Ultra Classic's doing the "wheels-up shuffle". It happens, and I for one am thankful for tose who have done so with the FJR to tell us that it happened and in what circumstances. This way we all have a chance to learn, albeit from someone else's misfortune.
Now, ride safe, ya'hear!