Let's imagine that one can actually "float" the scope, by whatever means: isolation transformer, a disconnected UPS, or whatever. One must remember that all BNC shells are now not at safe ground potential, but at whatever potential they are connected to in circuit. Remember too that they are all connected together; you can't just arbitrarily probe four signals by connecting the four ground clips to four separate points.
Here is another huge consideration: once you connect any/all of the "floating" ground clips to an arbitrary point in the circuit, all of the probe cables' ground leads and shields, as well as the chassis of the scope are (obviously) connected to that node. That's a big antenna, and a big conductor to provide capacitance to actual ground (i.e. to most other conductive things in the area). In other words, you will inject a large amount of RF into that node, and you will load that node with lots of pF to ground, much more than any proper differential probe would do. Even a correct probing technique can load a circuit to the point that the measurement can't be taken as 'truth' without consideration of the loading. If anyone thinks that the act of connecting a "floating" ground clip to an arbitrary node will not significantly affect the circuit, he is a fool.