For LOC-DME approach (back course) at Yakima Air Terminal (KYKM), NoPT was mentioned at different locations on this 2008 plate:
Click for full plate. Source.
However there is no procedure turn at all. Why is NoPT mentioned?
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FAA_H_8083-15B Instrument Flying Handbook 2012
Procedure turn. A maneuver prescribed when it is necessary to reverse direction to establish an aircraft on the intermediate approach segment or final approach course.
This particular approach doesn’t have a course reversal—the DME arc takes care of the course change from the YABLU IAF and the DATVE IAF. (Cut off on your map.) BABRE is an intermediate fix, and again needs no reversal.
So as you mentioned, there is no reason to state NoPT.
The version of the chart you used in your post is out of date. The current chart doesn’t mention NoPT, probably because there is no reason to. I’m guessing that mentioning it on your version is a mistake that they have since corrected or they are conforming to newer standards for chart making.