Absolutes
The DFW 35R Cat III ILS example interested me. I do not have access to my charts at the moment. But I would reason that the Cat III Chart shares most items in common to the CAT I chart for the same runway, and I would “guess” the CAT I approach plate for DFW 35R would have an IAP (or several) published. Therefore IAP fixes are published for that runway using that localizer.
I would say FlyBoyFloyd you are right; I like your logical explanation.
Several others answered the vectored for the approach situation well; you are being let to the intermediate portion by ATC.
The older I get the fewer absolute statements I make; for example “Every approach must have an IAP published” or “All published approaches have an IAP”.
I would not call you a first officer monkey. I have been in the right seat; now that I am in the left seat let me make an absolute statement. I don’t have all the answers. And you know that the people sitting next to you do not have all the answers all the time either. Being an instructor at the airline level is a license to learn (been there done that).