Need advice on LED strips wiring

That analogy doesn't work here.
In both PSU's, there's a transformer that effectively disconnects the AC side from the DC side. They're only virtually connected through the mutual inductance of the coils in the transformer. This means there's no common potential reference anymore. Any kind of external influence (e.g. build up of static, like you get on a woolen sweater on a dry winter's day) can make one PSU drift in its absolute potential compared to the other.

Try 'galvanic isolation' perhaps in combination with 'common ground' or something like that.