Grounding and shielding is still complex enough that half of it is best treated as voodoo, that is to say reason and analysis often rely on too much information that you don't have at hand :^)
Shielding acts to intercept electric fields, including the electric component of electromagnetic radiation (radio, TV, cell phone, etc) by draining the induced current to ground. The ideal shield would fully enclose the electronics. So to be effective, a tube shield must be connected to the chassis so it acts like part of the chassis.
Having said that, I hasten to add that the EF86 has an internal shield that surrounds the actual tube elements and is connected to pins 2 and 7. Those pins are grounded (p.60 in my manual) to T21 and T25. The external shield is redundant, and serves only to slightly improve the shielding - neither shield completely encloses the tube.
Incidentally, and for clarity, the 6922 has a different sort of shield. It merely separates the two triodes from each other, it does not surround them or separate them from the external environment. As we found out when developing the Seduction, the 6922 types need an external shield when in the presence of electrical interference.
Hope that helps a little!