Hugh,
I'll reiterate that I think this is a technique that can sometimes be used to estimate your position. Like many navigation techniques, it's not very accurate, because we cannot accurately measure slope angle from map or ground, and the resulting error bounds of the measurement mean that a precise position fix is unlikely. Thus, like many of the other techniques, we have to use it in combination, to fuse a number of position estimation methods into a more reliable estimated position*. Even then, I don't think it's ever likely to give us a result as accurate as a good resection/triangulation (which, itself, has accuracy issues when taking bearings, identifying features, and plotting the bearings).
A good example of where the technique would not work would be climbing up a ridge with uniform slope. Whilst you'd have a linear feature or well-defined slope aspect (the ridge), you would not be able to determine your height or position using the slope angle, because the slope angle would be the same all the way up the ridge. You would have to determine your height by other means.
It's certainly true that the technique can be used, just not in all situations... So I think only a minor revision of the UNM text would be required, along the lines of 'the technique can sometimes be used to provide an estimated position provided the slope angle is sufficiently unique'.
* By the way, even a GNSS receiver does this sort of fusion; it makes estimates of the reliability/accuracy of the signals from each satellite (based on signal strength and position in the sky), and weights the solution in favour of the better signals. The resulting position can be considered a strangely-shaped 3-dimensional probability density function (PDF), which, in turn, can be used to indicate the dilution of precision (DOP, or 'goodness of solution'); the broader the PDF, the larger the DOP, and the sharper/narrower the PDF, the lower the DOP.