III.83: Such were the three opinions brought forward at this meeting; the four other Persians voted in favor of the last. Otanes, who wished to give his countrymen a democracy, when he found the decision against him, arose a second time, and spoke thus before the assembly: "Brother conspirators, it is plain that the king who is to be chosen will be one of ourselves, whether we make the choice by casting lots for the prize, or by letting the people decide which of us they will have to rule over them, in or any other way. Now, as I have neither a mind to rule nor to be ruled, I shall not enter the lists with you in this matter. I withdraw, however, on one condition---none of you shall claim to exercise rule over me or my seed for ever." The six agreed to these terms, and Otanes withdraw and stood aloof from the contest. And still to this day the family of Otanes continues to be the only free family in Persia; those who belong to it submit to the rule of the king only so far as they themselves choose; they are bound, however, to observe the laws of the land like the other Persians.
When you say "Does this apply to modern day", do you mean to ask whether it is still the case that the family of Otanes "submit[s] to the rule of the king only so far as they themselves choose [and] continues to be the only free family" in modern-day Iran (or Afghanistan, or Iraq, etc.)?
If that's really what you're asking, then the answer is of course that there is no longer an Achaemenid Empire, there is no longer a king of Persia, and there is no longer a Persia in a strict sense. The Achaemenids ceased to exist over two thousand years ago. Otanes and his family appear only in the context of the 6th and 5th century BCE Achaemenid Empire. Here's a list of them. The fifth century BCE is when Herodotus was writing; that is why he says "still to this day".