Oscillscope Ground (Not Blowing it up)

After watching that interesting video... I presume all this applies to Oscilloscopes that are powered via the wall socket? For example....

Attach your Arduino to the USB cable which is hooked up to your PC. - now attach the GND probe from an oscilloscope, to the + rail, it will "short" because it's shorted
to earth (as described in the video).

But my question is, if it's "Isolated" it's safe... does that mean ALL portable Oscilliscopes (not connected to the wall to power it) are safe?

No. Safety can be lost due to complicated reasons. There are a hundred possible unsafe things that can be done with battery powered equipment. There is not enough time for me to give a blanket safety statement. But I do have time to answer specific questions, like this:

Can I put the ground clip of my battery powered oscilloscope to the +3.3 volt pin of Arduino if there are no other connections to anything else in this apparatus?
Yes. It is isolated.