It's amazing how often this subject comes up.
We are now at the same point (I mena, you and I are completely agree) does connecting any earth lead to ground (scope or dmm etc. test leads ) to any device (isolated or not) is dangerous.
That's an over-generalization. I will try to explain my opinion in more detail.
The problem occurs only when you are attempting to connect your scope ground lead to something that is NOT ground.
When working with a DUT that is grounded (especially if as in most testbenches it is on the same circuit as the test equipment), or even if it is not grounded (ie: battery powered, isolated by it's own or external transformer). It is perfectly acceptable and in fact normal to connect your scope lead to ground on the device.
When you decide to connect the grounded scope clip it to something that is NOT ground, there are two distinct but related issues that you have to deal with.
1) If the device is grounded, and you are connecting to something NOT grounded, then you are effectively shorting whatever you are connecting to ground. This will cause current to flow, which depending on the setup may a) blow a fuse, b) vaporize a trace in the DUT or your scope c) cause a major failure in the power supply of the DUT d) get hot/start a fire e) etc...
This is easily circumvented by placing either the DUT or the scope (see below before complaining) on an isolation transformer thereby cutting it's connection to ground.
2a) If you isolate the scope and connect it's ground clip to something NOT ground on the DUT, then any exposed grounds on the scope now sits at whatever voltage offset you clipped the lead to. This can make your scope hazardous to touch.
2b) If you connect your grounded scope clip to something NOT ground on an isolated power system, you are grounding that system at a point where it was not intended, which sets any exposed grounds on the DUT to whatever voltage offset you clipped the lead to. This can make your DUT hazardous to touch.
In your example, with the 300+V power supply, I would not want something with 300+V exposed "grounds" sitting on my bench, therefore I would consider "floating" to be hazardous.
If it was however a 5 or 10v power supply I would not have a problem with the arrangement, because accidentally coming into contact with 5 or 10v would not present a hazard.
In other words, issue #2 usually doesn't present a major problem with low-voltage devices.
(It should be noted that dropping a metal tool in the wrong place - say between the floating DUT and another grounded piece of test gear can still cause sparks and destruction).
In days of old, when differential probes and scopemeters were generally unobtanium, many people decided to "float" their scope on an isolation transformer, and then start happily measuring non-ground referenced things in the 300+V secondaries of classic tube televisions and the like ....
The scopes they were using looked like Photo#1 (OldTek.jpg). Note the large metal box, metal trim around the front panel, and many of these vintage scopes had one or more metal knobs. All now sitting at the 300+V that they had clipped their ground lead to. (Disclaimer - I don't have any scopes like this any more - photo snarfed from the web).
Not surprisingly some of them died!
Thus was born the adage "float the DUT not the scope".
Or course, this caused the problem that the large metal chassis of the TV was now sitting at 300+V relative to ground (as described above), but since many of these old sets had "hot" chassis which repair shops were used to, it was still the best solution - best to have one large hazardous hunk of metal on the bench instead of two. (and the metal scope was REALLY BIG).
Photo#2 (Abomination.jpg) shows something currently sitting on my bench. This (among other things) is a high power speaker amplifier. It is quite high power and has some fairly unpleasant voltages inside. Since it's a bipolar driver, there are times when I want to look at things not relative to ground. It is also attached to speakers, input sources (signal gen. etc.) and debug devices (ie: a PC). While I could try and float "everything" it's not really practical to float this DUT.
Photo#3 (TDS210) shows a more modern scope (still more than 20 years old). You can see that things have changed a lot. There is no longer metal case, there is no longer metal trim. No metal knobs, the plastic knobs do not have metal setscrews. The only exposed connections are the BNC connectors and the probe calibration output. As you can see in this case, I have attached a probe with an insulated BNC, and capped off the other BNCs and compensation output. It's pretty hard (but not impossible) to come into contract with a ground in this configuration.
For a while (before I decided it was still not a great solution) I used this on an isolation transformer when I had to look at non-ground referenced things up to a couple hundred volts, above that since the scope front panel does not have an insulation rating, I wouldn't do it. And I just didn't like fondling a device that I knew was improperly connected at unpleasant voltages.
Just for the record, I AM NOT recommending you float a scope like this - but (and I know lots will disagree with me), I do not think this particular arrangement is more hazardous than floating a DUT (which will often be something new that you are not familiar with), and in many case can less hazardous (but still hazardous).
Photo#4 (ScopeMeter.jpg) shows what I currently use if I need to look at something not ground referenced. The Fluke is great for probing like a scope, the UT-81 is handy as a graphical DMM.
EDIT: You might think that these being just "scopes that run on batteries" are not much different than the transformer isolated bench scope. There is however one BIG difference, which is that these are rated for HV application. They are much better insulated than a bench scope (eg: the BNC's on the Fluke are insulated on the outside so it's hard to contact them even if not capped), and that insulation has been tested/certified for the device rating.
Photo#5 shows the other good solution, a differential probe. (I also don't have one of these, photo snarfed from web).
Whew!
Dave