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!