I could't say that I believe that there has to be a rule to it. There're some nuances we should be aware of.
QUERENT taking the question
If the querent determines the horary question time - this HAS to be a trained and experienced querent, because one has to be able to recognize a horary moment - that moment of genuine interrogation, voided-minded, when the globe stops spinning and all we live for is the answer to this question (I exaggerated a bit, but you get the idea).
The querent must then be intelligent and able to phrase the question in a clear and concise manner, while still introducing enough details so that any confusion might be avoided.
Also the querent's clock must be most acurate, of which the astrologer cannot be sure...
If these conditions are fulfilled, then the question is pure and clear and the chart ready to be interpreted.
ASTROLOGER taking the question
I noticed there're differences in the "feel" of sample horary charts I could find in the books already published and the "feel" of my own horaries, set for the moment when the question was addressed to me. This is quite understandable because when the astrologer receives the question, he becomes a part of it, the other person to whom the question is addressed to. Actually the horary chart displays him/her in the 7th house and provides information on astrologer's ability to answer the question at that particular moment as well as to the success of this delineation (as considered by the client).
So, there will surely be some horary chart differences from astrologer to astrologer, as this is also an event in the life of the astrologer.
Also, the astrologer might ask suplimentary questions to the querent or guide the querent to phrase the question until the inquiry becomes clear - this is the moment to be considered as a horary moment and have a chart constructed for it.
Not to mention that the astrologer, fully aware of the importance of exact timing, will set the clock to be accurate all the time.
Now, about this debate whether the querent or the astrologer should set the data for the horary chart.
There're clearly extra advantages to having the astrologer receive the horary data, as pointed out above, but the question is more pure when the querent is the only one invoved in the chart, so I'd trust Lee Lehman when she states in her book that she prefers having the querent take the chart data, if the querent is a trained and experienced horary inquirer, but when it is not the case, or the astrologer has doubts about that, using the astrologer's time is the wise option.
So, I wouldn't cast my vote on the poll.