The point is, everyone is convinced (and I don't dispute) that the stray signal is on the center battery, and not the others. If that's true, what's the difference with the other two batteries? If there is no signal on them, why not connect/short/bond/whatever you want to split hairs on, the cases together, so that however the outer batteries are eliminating the signal can be shared by the center battery? Because IMO that's all you're doing with the tape, otherwise the people who put the foil under the foam would be seeing the same results.
I agree that you are probably right, but some people might see the word "ground" and take a wire to somewhere it shouldn't be (as darunimal stated).