It is possible to get into trouble by measuring only hot to ground. It is necessary to always measure hot to neutral, or in the case of a 240 volt circuit, hot to hot, to verify correct operation of the circuit. In the case of three phase power (rare in residential service), it is necessary to measure voltage between the phases, and voltage between phase and neutral. Many three phase services do not have an independent ground, for those services hot to ground has no meaning (in many three phase services, the neutral is grounded, but not always).
A recent near fatal incident at West Valley, NY (a nuclear waste storage site I worked at) shows measurement issues. The electrician was assigned the task of removing a presumably dead three phase service from an abandoned building. He checked phase to neutral for all three phases, and reported zero reading. There was no independent ground on the service. He then attempted to remove a portion of the service. Fortunately he was wearing full arc flash protective equipment, as he dead shorted across two phases, and welded his wrench to the bars, and sustained limited injury (no arc flash gear, he would likely have died). In the accident report, the proximate cause was improper zero energy check. Apparently the electrician never measured phase to phase voltage, and the neutral was disconnected, thus phase to neutral produced no reading.
A somewhat similar incident occurred recently at a nuclear plant in South Carolina. The electrician was assigned the task of removing a defective lug from a three phase service. He followed standard zero energy test procedures, by measuring voltage from phase to phase, and phase to neutral (there was no independent ground). In all cases, the reading was zero. Upon attempting to remove the damaged lug, there was an arc flash, leading to limited injury to the electrician (he had on full protective equipment). The proximate cause of the injury was improper voltage detection procedure. It appears that the particular voltmeter he was using had a button which allowed a remote reading to be captured. This technique had been used previously when measuring voltage in a difficult to access area, and the zero reading had been locked into the machine. Despite the presence of a low tone and a small LED light, the electrician failed to note that the zero readings on the live three phase service represented a locked reading from a previous measurement.
Despite the fact that stringent safety procedures are in place at all nuclear plants I am familiar with, and despite the fact that trained electricians perform all work, serious and even fatal accidents continue to occur at nuclear plants in the performance of routine electrical work. So how does this relate to measurement at home?
I am relatively certain that the average homeowner does not have a written check list procedure for measuring voltage. They probably do not employ exactly the same procedure each time. They probably do not employ stand down procedures if the reading they get is not what was expected. They likely do not use standardized lockout and tag out procedures. They almost certainly do not have arc flash protective equipment. They probably lack professional training. What is amazing to me is not that accidents occur, but that electrical accidents are not more frequent. Possibly this is because the average homeowner is uncomfortable around electricity, and perhaps does not undertake more complex and dangerous tasks such as installing a service, or installing a panel. Plus very few homes have three phase service, and at least in the U.S. voltage is limited to 240 volts in most residential services.
As to the question originally posed, it should certainly be part of every zero energy check to measure leg to leg (240 volt), leg to neutral, and leg to ground. It should also be part of every zero energy check to verify correct operation of the instrument by testing a known source first. I don't know why anyone would suggest that there is a reason not to test leg to ground. It is essential that the individual stop for a minute to consider the results of the zero energy check after performing it. Were the results as expected? If not, DO NOT PROCEED further without a full understanding of exactly what the readings indicate.