"Ground" is a concept. It's convention; that is we agree on the definition. (I know, agreement is a foreign concept to you...just go with it.) We drive a metal stake in the earth and call it ground. If you don't put any current in the stake, you can use it as a reference for all measurements. If you need a differential measurement, just measure the two relative to "ground" and subtract. Works just fine in concept.
As a practical matter, it takes much less "technology" to make a local single-ended measurement relative to a "common" point. That common point is often pretty close to "ground"...doesn't have to be, it's just easier to work with and easier to make safe.
This paradigm creates systems that are "safe" in most cases, when they're working properly and are still safe under the most common fault conditions as long as you leave the covers on the system. When you open the box, many safety assumptions don't apply.
There are exceptions, but when you use an isolation transformer to "disconnect" the local common from the conceptual "ground", you don't necessarily make a properly functioning system any less "safe" under normal operation.
An Isolation Transformer is not inherently unsafe. But an isolation transformer does NOT make a faulty system SAFE to poke around inside.
What IS unsafe is the stupid things people do with their hands and test equipment believing that the transformer absolves them from any responsibility to THINK about what they're doing. Redefining your own common reference by attaching an arbitrary node inside the faulty supply to your local concept of "ground" is decidedly UnSAFE.
While I'm on the subject of RESPONSIBILITY... People ask questions because the don't know the answer. In many cases, they can't even tell if the advice they're getting is good or bad. One way is to vote. If two, or three or four people said it, it must be true. Problem is that the most vocal newsgroup denizens are demonstrating the least ability to think about and understand the consequences of their advice. And there are WAY more than two people giving bad advice here.
One way to judge advice is the tone of the thread. Name-calling is what you do when you don't have a logical leg to stand on. A spirited, yet civil, debate often leads to consensus. That advice is more likely to be helpful. As soon as the name-calling starts, you can't trust any advice from the thread. Some of the input may be helpful, but you can't tell which, or you wouldn't have had to ask the question in the first place.
We have the responsibility to do no harm, and argue logically against unsafe advice.
Doing stupid, unsafe things may work 99% of the time. As long as that 100th time is YOU, I don't have a problem with the odds...I'd buy a ticket to watch. If that 100th time is some innocent guy who took your bad advice, I have a BIG problem.