I wouldn't worry too much about whether the scope is grounded or not. If it originally had a grounded plug which has had the ground cut off or been replaced with a 2-prong plug then it should be replaced with a grounded plug. If it was never grounded to begin with then don't worry about it, it's ok that it's floating. When people speak of "floating a scope" they often mean deliberately disconnecting the ground in order to use the scope to measure a high voltage non-isolated device, this is dangerous, not the fact alone that the scope is floating. So long as you are staying away from the mains side of whatever gear you're working on then there should be no problem. A good rule to follow is if you wouldn't touch something with your bare finger, don't connect a scope to it.
No, that is dangerous advice: it presumes an ideal world with complete knowledge and complete understanding.
If there is a mistake, or a misunderstanding, or a fault, then a floated scope can be lethal.
Example mistake: a probe slips.
Example misunderstanding: you misread a diagram, e.g. not recognising whether a protective mains earth connection is specified.
Example fault: mains has jumped to an unexpected place in the UUT - and that's why you are probing it in the first place.
And with a little imagination or knowledge, many many other examples can be found.