HI Oskar,
I've sent you a PM, but it would be good to get a bit more info on the age of this system. There was a known issue that caused something like this with some early handles. It was corrected, dealer stock was replaced in those cases. If this is that problem, it looks like yours was missed.
It is normal for the handles to have a bit of flex in them, which some people don't enjoy, and is amplified with heavy strobes or video lights. The handle bracket has been added as an optional install to knock that out.
Moses, I wouldn't worry about the strengths of those the handle bolt attachment. They brackets are optional, and something like 20 models used this tray prior to their being added.
Handle brackets were never offered for E-M5. The mounting holes you see on the right grip are for an accessory hand strap, not a bracket. I'm confident that once you get a current handle this won't happen again.