It's definitely possible since most of the people of the ancient world lived in Turkey, Egypt, and what we now call the Middle East. In the ancient world, this area is called the Near East by modern historians since it is the east part of the world near "the west". It is weird that it would be that high because I don't know how they would keep track of that, especially if they were using Herodotus' bad numbers.

So more than just knowing the percentages of population the Persians controlled, one should keep in mind that they controlled a lot of territory during their reign. At their height, the Persians controlled all the land in Asia from Iran to Turkey to Egypt and Parts of Saudi Arabia. This was a lot of land for this time period and lot of population. Additionally, it should be noted that the Persians controlled their subjects through tribute based rule. So this means the Persians collected tribute from their territories and levied men when needed, but they were not actively in involved in each region's affairs. Which also meant they did not keep the best census like the roman censors 500 years later.

So it was very likely that the percentage of world population the Persians controlled was an estimate more than anything. We just do not have the sources to confirm them controlling that much population of the world at this time. So I would not worry about those population numbers too much.