OED says that this use of the word consulting does in fact mean giving advice and stems from a now-obsolete sense of the French consulter, to give (professional) counsel. They suggest that the word should be parsed as a noun used attributively, rather like "loudspeaker" in "loudspeaker cabinet", "a cabinet for a loudspeaker". Thus a "consulting engineer" is an engineer to whom one goes for a consulting.
2: Applied to a physician, engineer, etc., who makes a business of giving professional advice, either to the public or to those practically engaged in the profession. [ < French médecin consultant, ‘celui qui donne des consultations’ (Littré); from obsolete sense of consulter to give (professional) counsel: compare “consultation” n. 2c. But as now used consulting would be understood as an attributive use of the verbal noun.]
The action of the verb consult; consultation. Also attributive, as in consulting room.
However, this is the only way in which the word consulting is synonymous with anything to do with advice. The normal uses are as quoted in the question: one consults someone who advises, and the words are practically antonyms.