There were stories about the family being tax collectors in the municipality of Nigtevecht, but I have never found proof of this. It is, however, possible that the Huydecoper van Nigtevecht family had certain rights, freedoms, and duties related to raising taxes in the area as "Lordship of Nigtevecht" from the Dutch "Heerschap". Hence the description "Huydecoper Lord of Nigtevecht" or "Huydecoper Lordship of Nigtevecht". Dutch titles can be confusing in English, as they have changed over time. The use of the Dutch "Heer" can also be confusing; it depends on context.
heer / mijnheer = mister, common use of sir
Lower nobility title "Heer" or "Jonkheer" = Young Lord, but often used as Sir
High nobility title "Heer" = Lord, Lordship. (Also used in the Bible as Lord of Israel, Lord Jesus).
There are more stories associated with the name Nigtevecht for which I have found no proof. One of these is that a naval vessel called "the Nigtevecht" ended up in the fleet of one of the Kings of England together with a vessel called "The Vreeland". However, I found old records of ships loaned from the Dutch to English kings but no evidence of this, nor of them being seized by the English. This must be incorrect because VOC ships were merchant vessels, not naval ships. There were VOC ships called Nigtevecht, Vreeland, and Breukelen around 1650; this information is easy to find. There was also a vessel captured by the English Navy called the "Hilversum", which was then incorporated into the English Navy. Oddly, that bears the name of the place where I was born.