The outside of the tube is generally earthed using a couple of springs
stretched across it, and it should be obvious if these have become
detached. In fact, I've never seen this happen.
I've seen a lot of different attachment methods. You are thinking here,
obviously, of gross mechanical disconnection. Yes, that would normally
be obvious and, yes, it should also be rare. I agree on both points ...
but have you considered the assumptions between that and taking the
outside of the tube as being at a safe potential?
Consider, if the attachment involves one or more metal-to-metal connections,
and especially if those metals are not the same, then poor connections can develop
at the joints/attachment points/connections by any of several means, such as
oxidation or corrosion. This can lead to a poor connection with NO visible
signs or with signs visible only upon close inspection. (Remember that
abhomination of using aluminum wire for electrical distribution?) If the
equipment has been exposed to moist air for some time, poor connection becomes
quite likely. A TV set left in an unheated or poorly heated summer beach house,
could verly likely have poor grounding connections due to corrosion in such
an environment. We do NOT know the history or envronment of the set the OP
was asking about, let alone other sets that other novices may consider probing,
years hence, after viewing these message out of the Google (or other) archives!
I repeat, you do NOT know that the grounding is good. It is an assumption.
It may be a very good and reasonable assumption, and if you were the one to
be considering probing the innards of the TV set in question, it would not
be an issue. But the OP was clearly a novice, the set in question is known
to have problems, and in such a combination of lack of experience and known
circuit misbehavior, I thought it best to raise all possible safety issues even
if the failure modes leading to unsafety were rather unlikely.
MY personal safety rule for working with HV circuits is to assume that ANY
PART may be at HV until proven, by measurement, to be safe. I will continue
to recommend that approach to others. You can, of course, choose what rules
you wish to use when working on equipment at home. My personal rule was
cemented when I worked at the High Voltage Research Lab at MIT, where even 30kV
is not considered really HV. So it is, perhaps, a bit overcautious for mere
probing in a consumer TV set. But it is better to be more safety conscious than
needed rather than the other way around. (Again, MHOO; YMMV.)