Have also noticed poor CMRR on the BM235, mainly just an issue when probing a heatsink / transistor tab / pin and the TC ball touches a switching node and the reading goes kablooie. Seems fine as long as it's not touching. In your case, probably it's similar immunity (or lack thereof), but being nestled down inside a network at even higher voltages*, it has similar effect.
*In my case, switching nodes, so, 100s kHz at 100s of V, but harmonics in the 10s MHz range then are only some ~V. So your case is probably the more aggressive -- give or take if it's more sensitive to impulsive or CW noise, or what effect those have on the acquisition, etc..
Tim