This seems a like a pretty strong claim. I hope that it's true, but I'm not going to be running WASM modules in ring 0 any time soon.
What probably has the most bearing on the securability of a platform is its simplicity, which is on WebAssembly's side.
When I first read the specs, it screamed to me "VM design 101." It feels to be someones master thesis, more than a piece of production software. Just as the original Netscape Javascript 1.0 was.
It will have its fair share of "typeof null" style bugs to come.
Who knows what was in their heads, but stack level attacks are as easy as to exploit unsafe type casting in anything that amount to a stack pointer.
My guess why they choose to do it that way is simply because there are more literature available for mid-tier coders in style of "VMs for dummies" and they wanted to always have an option to not to do extensive research on every small mater, and just copy JVMs behaviour.
The security problems of java are not related to it being a stack-based VM at all. The problems are that the api lets applets do things they shouldn’t be able to and arbitrary code execution during serialisation.