There's also the notion that the Dutch grammar has been changed quite a bit over the years and used to resemble German a lot more. Mostly things are a lot simpler these days than they used to be. Older Dutch texts are hard to read even for Dutch people. Even texts from the 19th century look very different from modern Dutch.
Finally, the reason English speakers recognize a lot of Dutch words is because a lot of English words actually have Dutch origins. For example, the word cookie is a bastardized form of the Dutch koekje. Especially a lot of naval jargon comes straight from Dutch. The reason for this is long trade relations, colonizing the same places (e.g. New York used to be New Amsterdam), etc. There even was a Dutch king on the British throne in the seventeenth century.
