I think you have to parse the sentence from the NEC to see if it works.
The first question is, what is meant by "fastened in place". It is important to note that a piece of equipment can be both cord-and-plug-connected and fastened in place.
210.23(A)(1) discusses requirements for cord-and-plug-connected equipment not fastened in place.
210.23(A)(2) discusses utilization equipment that is fastened in place, and the restrictions on load where lighting units and/or cord-and-plug-connected equipment not fastened in place is also supplied.
Every dishwasher (except the roll-around kind) and every disposer that I have ever seen was fastened in place. A dishwasher that I installed last week was fastened to the bottom of the countertop, and the disposer was certainly fastened in place at the bottom of the sink. In that case, the restriction of 210.23(A)(2) does not apply.
Therefore, the limit on whether you can connect a dishwasher and a disposer to the same circuit depends on whether the total load exceeds the branch circuit rating.
My dishwasher is rated at 11.5 Amps and the disposer at 8.1 Amps for a toal of 19.6 Amps. They are both legally connected (hard-wired) to a 20 Amp circuit (circa 1965).
One restriction on using a receptacle is that there is a code section (I am not going to search for it now.) that requires that cords for appliances be provided or approved by the appliance manufacturer. Most dishwashers and disposers don't come with cords. I would plan on using a piece of AC or MC, or LFNC.
In the new house where I installed the dishwasher last week the licensed electrician had provided a 5 ft length of 14/2 NM (Romex) coming up through the floor at the back of the dishwasher space.