Why is it safe to touch the chassis of a tube amplifier and something earth grounded simoultaneously?
Warning


FYI -  some early AC/DC radio sets had live to mains chassis when operated from mains. 




Equipment chassis is usually grounded to wiring ground via earth lead on power plug where provided. 

In any sane regulatory environment, appliances without an earth lead are required by law to be "double insulated" so that internal metal parts are not touch accessible during operation. (Note: Double insulation nowadays seldom involves two layers of insulation - it is more a state of mind in manufacture and testing that leads to touch safe equipment. Usually :-). )

While a chassis should be "touch safe", never assume it is, because:


There are non-sane regulatory environments, 
or ones where the authorities enforce the rules so little that they may be ignored and 
It is excessively common for people  to do silly and dangerous things with mains wiring, despite being aware that people are reported to have died due to such things.




Wikipedia - appliance classes

They say:

Class I 


These appliances must have their chassis connected to electrical earth (US: ground) by an earth conductor (coloured green/yellow in most countries, green in the U.S., Canada and Japan). A fault in the appliance which causes a live conductor to contact the casing will cause a current to flow in the earth conductor. This current should trip either an overcurrent device (fuse or circuit breaker (CB)) or a residual-current device (RCD) also named as residual current circuit breaker (RCCB), or (ground fault circuit interrupter (GFCI)) or also, residual current operated circuit-breaker with integral overcurrent protection (RCBO). which will cut off the supply of electricity to the appliance.


Class II  - See also: double switching (and double insulated)


A Class II or double insulated electrical appliance is one which has been designed in such a way that it does not require a safety connection to electrical earth (US: ground).

The basic requirement is that no single failure can result in dangerous voltage becoming exposed so that it might cause an electric shock and that this is achieved without relying on an earthed metal casing. This is usually achieved at least in part by having two layers of insulating material surrounding live parts or by using reinforced insulation.

In Europe, a double insulated appliance must be labelled Class II, double insulated, or bear the double insulation symbol (a square inside another square)..


Class III


A Class III appliance is designed to be supplied from a separated/safety extra-low voltage (SELV) power source. The voltage from a SELV supply is low enough that under normal conditions a person can safely come into contact with it without risk of electrical shock. 

The extra safety features built into Class I and Class II appliances are therefore not required. For medical devices compliance with Class III is not considered sufficient protection.