Well, count me in. I've just had my third center stand break, right at the weld as you have described. This pic is the first one that broke:
The second and now third center stands have all broken at that exact same spot.
It is due to a poor design that puts all the stress right at the end of the weld brace, and possibly poor welding (or at least not properly heat-treating the part to minimize these stresses right at the weld location).
The new K1300GT's do have a redesigned center stand, with a different foot lever and a different brace welded on in a different manner.
It does look much more robust. It also looks like it would be a direct bolt-on replacement, although I haven't yet been able to compare the two side-by-side on a bench or to try and fit one up on a bike.
The other problem, which actually made it to a Service Bulletin is the weak stops. This manifests when the stops bend under stress allowing the center stand to rotate too far forward. Note how the center stand is angled forward instead of being vertical, and the feet aren't sitting flat on the ground:
These are clearly two distinct problems, although it is possible to have both occur on the same bike (lucky me). It's especially annoying when you have a trip-loaded bike, no center stand foot tab, and bent stops such that even if you do manage to get it on the center stand, the rear tire is still on the ground. And then you need to pull the rear wheel to get a new tire fitted so you can make it the rest of the way home . . .
As for the local rep, simply remind him that all BMW parts come with a two-year warranty, so unless you broke it more than two years ago it should be replaced without question, at least with the original K12 part. You're on your own for getting them to fit the K13 part . . .
'13 Dark Graphite Metallic K16GTLD, 24K miles and counting...
'09 Magnesium Beige Metallic K13GT, 60K miles miles and counting...
'02 Mauve Metallic K12LTC, 106K miles and sold
BMWLT#145, IBA# 366, MOA# 111996, SCMA# 24032
All lower 48 states plus Alaska on the K13GT in two weeks . . .
Some people see the gas tank as half empty. Some see it as half full. All I care is that I know where the next tankful is coming from...