This paper by Cristiano Broccias contains a couple of clearer explanations of transparent adverbs:
- Sally angrily shouted at them.
- Sally angrily read the letter.
Angrily in (1) can be paraphrased as "out of anger." It stands for the motive which drove Sally to shout. Angrily in (2), by
contrast, refers to the consequence of Sally's reading the letter:
reading the letter made Sally angry. Geuder (2000) and Himmelmann and
Schulze-Berndt (2005) call such uses transparent.
Broccias gives a further example to illustrate that a transparent adverb is used to convey a consequence.
However, I'm not sure how to apply this criterion to the example that the OP cites:
- Conrad has not really left.
- Conrad has probably really left.
Really can be paraphrased as "in actual fact" or "in reality." However, it's difficult to see how it's either a motive or a consequence in either sentence.
Either Monika Doherty is not using transparent adverb in the same sense as either Broccias or Geuder, or her example isn't well-chosen.