The old clothes dryer receptacles were NEMA 10-30. This had two hots and a neutral, but no ground. That is because going way back nothing had grounds. As grounds were added (witness the progression over the last 75 years or so from most ordinary 120V receptacles having 2 prongs to having 3 prongs), clothes dryers were supposed to be migrated to NEMA 14-30, which has two hots, neutral and ground. But as a fallback measure to provide some limited protection and backwards compatibility (i.e., new dryer with old receptacle), clothes dryers were allowed to be installed with ground and neutral connected in the dryer. The presumption was that over time the receptacles would be replaced, and all new receptacles would be NEMA 14-30.
That worked for new construction. But for old construction, instead people got new dryers (they don't last forever) and continued to connect them to NEMA 10-30 receptacles. And it has gotten so bad that there are numerous questions here where people open up their "old" 10-30 and find that it actually has a separate ground wire available! And people continue to ask questions about how to convert their 4-wire receptacle (14-30) to 3-wire (10-30) because they got a used dryer that only has a 3-wire cable. When in fact the proper thing to do (and actually easier than replacing a receptacle) is to replace the dryer cord and remove the neutral-ground bond in the dryer.
On to the question:
GFCI in general is a great way to provide protection in lieu of ground. If you have a 2-wire receptacle with no ground available (no ground wire lurking in the back of the box or just outside the box, no armored cable, no metal conduit, no easy path to add a ground wire) then you can replace the ordinary 2-wire receptacle with a GFCI/receptacle and get substantially the same protection as a properly grounded receptacle would provide. Actually quite a bit better protection in certain respects. Note also that the receptacles are supposed to be labeled so that any user knows that this is not an ordinary grounded receptacle - i.e., if they truly need ground (e.g., for surge suppression) then the ground pin is not connected and therefore useless.
However, a clothes dryer is a different beast. You can't put in a GFCI/receptacle because nobody (or at least nobody that I've found) actually makes one. If you could do that then you would remove the neutral-ground bond in the dryer and install a 4-wire (ground not connected because unavailable) 14-30 GFCI/receptacle and be reasonably protected just like a 120V NEMA 5-15 with GFCI. But that isn't an option.
So the next best option, and required by NEC 2020 for new circuits, is to install a GFCI/breaker, like the Siemens referenced here. The problem is that if you combine it with a 10-30 receptacle without ground and a dryer withe neutral-ground bonded then you will have a false sense of security since a ground fault will go to neutral and not be seen as a problem by the GFCI. Using a GFCI/breaker would actually hide a very real problem. In theory the GFCI would still help in case of user touches dryer with ground fault when it is on, but it is far from an ideal setup.
In addition, there are only three groups of people who are likely to install a GFCI/breaker for their clothes dryer circuit:
- New construction under NEC 2020 rules - 14-30 is mandatory, since 1996. So this warning says "don't cheat".
- New circuit in old construction under NEC 2020 rules - 14-30 is mandatory, since 1996. So this warning says "don't cheat".
- Owner is a safety fanatic and wants the best protection (e.g., they just bought a house and are fixing all the old problems and getting everything up to NEC 2020 code even where not strictly required). This warning says don't put in the GFCI/breaker unless you also replace the old receptacle. Which is very good advice.
I find it extremely unlikely that someone would decide to simply add a GFCI/breaker to their clothes dryer circuit as a half-way measure to improve safety. Those breakers are expensive, the solution is not perfect, replacing the receptacle is the right thing to do anyway (how many people are using pre-1996 dryers and really want to put in 240V 30A GFCI breakers?), and I'd bet that in almost all pre-1996 homes (because afterwards any 10-30 should be an improper retrofit and a ground wire hiding in back from the original 14-30) that I've seen, the laundry room is in the basement and electrical, including running either a new cable or at least a ground wire, is easy to do. The older the house, the more likely that is the case.