The Mazda trailer hitch has the receiver tube integrated into the assembly, if that is what you are asking. It does not have the ball mount, hitch pin, safety chains, brake light harness. Note the part number for the 2017+ trailer hitch is 0000-8E-R06A.
You can also see the Parts of trailer hitch which is a great primer.
I would agree the ball mount is not included in the price of the receiver, but the OP should speak to a couple of dealers because it is so freaking hard to get to an online parts catalog. I am spoiled by the multitude of Honda/Acura on line parts catalogs...
And of course, neither is the wiring harness.
It is just me, but I would consider a non-OEM Class 3, 2-inch trailer receiver, rather than the OEM 1.25 inch receiver. For me, not that I tow, but when we did a lot of bike riding, the 2 inch bike carrier tube seemed to be standard. It was really sort of hard to get a 1.25 inch bike carrier for four bikes, and the accessory converters 1.25 to 2 inch can be loose fitting, putting a lot more play into the assembly, as well as moving the whole carrier further away from the car center of gravity.
I just installed the OEM hitch and wiring harness on my CX-5. I can definitely confirm that there is no receiver. FWIW, I really prefer the look of the OEM hitch to the aftermarket hitches which hang down below the bumper cover, but Chas makes good points about the 1.25" receiver limiting some choices.
You will have to cut the bumper to install the OEM bumper. I used a jig saw with a scroll blade designed for cutting laminate. I imagine that any fine toothed scroll blade would work though. Cutting a bumper is nerve-racking. Last time I tried, I found it difficult to un-cut something. It came out fine though. The parts come with a template. You barely notice it's cut from a standing position. I took a picture from down low to show the cut better. One thing I'm curious about is the '16 template was a smaller cutout than '17 and up. I assume for chain clearance and wires, but the smaller hole would've looked better, I think.