unfortunately, for denmark, it's not true, nor do i even know where the clam of 800 years comes from, as it's hard to even make sense of. there were no europeans in greenland, recently, until 1721, when a danish expedition was sent to find a lost norwegian settlement. while that is still 300 years ago, it's worth pointing out that jamestown was founded in 1607, quebec city was founded in 1608, new york (as new amsterdam) was founded in 1624, boston in 1630, montreal in 1642, philadelphia in 1682 and detroit in 1701. the danish were actually late to american colonization.
now, it is true that there was an older norwegian settlement there, founded around 982 and certainly long gone by 1286. but it's also true that there were no europeans in greenland between the collapse of the norse settlement and the danish colonization in the 18th century.
i have no idea where the claim that greenland has been a part of denmark for 800 years comes from and it's clearly wrong.