> If the chassis is connected directly to live (quite possible on old TV's),
> and you hold chassis and an earthed scope, you have full mains directly from
> hand to hand - a path straight across your heart :-(.

Yes.  And "floating a scope" (i.e., removing its ground lead) is not good
practice.  As soon as you try to use some other instrument like a DVM or
signal generator and forget that it too is grounded you'll have the same
problem as with a grounded scope.

The correct solution is to put the TV on an isolation transformer.  This
should always be done when working on anything that might have a hot chassis.

Eric