That is correct.
Some (most) generators don't like surge protectors because Surge Protectors need a "ground" wire (to bleed off the captured spike). Generator's don't have a grounding rod (driving into the ground) - unless one installs a grounding rod and connects to their generator. To by-pass the non-bonded generators, some folks create a simple M to F plug (short pig tail) adaptor. Very simple DIY task. Within this adaptor, they simply "bond" the white wire and bare (ground) wire together. Thus, making the unbounded generator thinking its grounded. But, their generator still needs a grounding rod - to be fully grounded. Yes. The area of bonded and non-bonded (with each risks) is much more complicated than it appears. If wondering, Google Search will provide lots of official documentation on "generator non-bonded vs bonded" text string.