Should you answer 'are you interviewing elsewhere' honestly when you don't have other interviews yet?
Short answer: Yes, you should answer honestly.
Long answer: your question contains, implicitly and explicitly, several (mostly) flawed premises.
Premise 1: professors are superficial people who can’t be bothered to come up with their own idea of how good you are as an applicant based on the strength of your application, so will resort to relying on an (essentially) irrelevant piece of information to guide their decision.
The reality: almost no professor would care whether you have an interview elsewhere, or, to the small extent that they might care, it’s mainly to help them figure out if there’s any time pressure to reaching a decision on your application. In the case of truly stellar applicants the knowledge of other pending interviews/offers may affect the salary the professor might offer, but in normal cases it won’t.
There’s also a small number of professors for whom the assumption you’re making may be valid. But by and large the premise is not an accurate description of reality.
Premise 2: you are as good of a liar as you think you are.
The reality: you aren’t. In your question you only factor in the perceived cost of acting honestly (and are incorrect in how high you think that cost is, see premise 1 above) but completely ignore the very real - almost certain in my opinion - possibility that the alternative approach of trying to make yourself look much more desired than you are by not telling the honest truth would come across as clumsy and clueless in the best case, or shady and dishonest in the worst case. That eventuality will lead to a much worse outcome (certain rejection of your application, and a bad reputation that could follow you far into the future) than the eventuality you are actually expressing concern about.
Premise 3: if you say you don’t have any interviews you will have to accept an offer very fast since “they know [you] don’t have other options”, even if in the meantime you do receive some other offer.
The reality: this is false. You seem to have the misguided notion that by stating you don’t currently have other interviews you are committing yourself to never having any interviews. That’s not how the world (academia or anywhere else) works.
Hope this helps, and good luck with your interview!
In general, honesty is a good thing. But you can be honest without giving out too much information. Some possibilities that may work for you.
Not at the current time.
I'm awaiting some offers.
I'm only getting started in this process.
None that I'd care to discuss at this time.
But you can also turn it around a bit.
This is the one I'm most interested in at the moment. (a non-answer)
Not all of these are equivalent, of course, but you may be able to come up with something that fits your case.
To offer another perspective on the question; you may be attributing incorrect meaning to the question.
It may sound as if a question asking if you are interviewing other places is gauging how many other places 'want you', but may just as well be gauging how much you 'want them'. I.E., are you interviewing for other job opportunities that are completely unrelated to this one? Is this your main target?
For each example you think of that suggests they would think less of you, there are equal numbers of examples in which they are instead trying to understand your own interests (which links to how well you fit in their department) or even where they stand in relation.
So it is not a good idea to lie, as I can imagine the next question could even be "so where?". Academia is a small world, and it is likely they will know the other job openings.
Having been on both sides, I can say at least a few times there was a question of if the department could even attract a person, and understanding the state they were in for other offers was a way to rush their application through administration. Similarly to my last point, when there is a faculty position posting we also do an extensive search to find what other peer institutes are searching for, so it is usually expected someone is applying to other postings we are already aware of.