It does to Dutch ears too. Just a few weeks ago, I passed through some tourist-infested area in Amsterdam. "Are these Swedish tourists drunk at this hour in morning already? Oh, wait, they are sober Danes."
Does it? Now I wonder what Alemannic (Swiss-German, maybe especially the heavier dialects like Bernese and Walliserdeutsch) sound to you, because to my Bernese ears, Dutch sounds a lot closer to my own language than pretty much all other germanic languages.
It does to Dutch ears too. Just a few weeks ago, I passed through some tourist-infested area in Amsterdam. "Are these Swedish tourists drunk at this hour in morning already? Oh, wait, they are sober Danes."