It was actually translated into English by De Zwart himself. I believe that proper capitalisation of Dutch names with 'de' is to keep the 'd' lowercase if stating the full name (Hans de Zwart), but to capitalise the 'd' if stating just the last name (De Zwart), which the article seems to do consistently (except when quoting Facebook's mangling of the name).
In this context, Dutch refers to the country The Netherlands, not the language.
Based on my non-linguist opinion, I would say you're correct. Dutch people tend to not capitalise their Ds in surnames. When only mentioning the surname, it is treated as a mini-sentence, hence the capitalisaiton.
In northern Belgium (AKA Flanders), Dutch speakers tend to capitalise their Ds in surnames, so you would see "De Zwart" regardless of where it appears in the sentence. In case you're wondering: yes, there are quite a few surnames that exist both in The Netherlands with "de" and in Belgium with "De". The same goes for "van" (of) and "vander/van der" (of the), for instance.
Then again, if they're nobility, they might not capitalise the "de" because it might be the French "of" as opposed to the Dutch "de", meaning "the". Confusing stuff.
In Spain we don't have so many surnames prefixed with particles, but we do have some (e.g. "Del Río") and the capitalization also works as you describe for Dutch.
It makes sense: when you say Juan del Río it's obvious that it's a surname, but if you just said "del Río" without context, the "del" could be confused with the common word.
Works like that in French -- with subtle caveats depending on the length of the name and weather it starts with a vowel: "D'Alembert", "De Sèze", "De Gaulle"... but "La Rochefoucauld".
