That comes from Hagrid, who isn't exactly the smartest or most politically astute person around.

 

...Who has still been a citizen of the magical world and part of that community for decades. Are you going to ignore facts just because the person saying them is perhaps a little bit slow? You don't need to be super smart, knowledgeable or politically astute to know the main job of your entire fucking government.

 

It's funny how the Ministry has a Accidental Magic Reversal Squad, an Obliviator Headquarters and a Muggle-Worthy Excuses Committee, a Misuse of Muggle Artefacts Office, but a "Muggle Relations Office" is never mentioned. If not for the Minister of Magic to Prime Minister encounter, one could think the MoM doesn't even recognise Muggles have a government body.

 

Because it doesn't and shouldn't exist.

 

There's the Muggle Liaison Office. I'm pretty sure they were responsible for the Prime Minister shenanigans in HBP.

 

It should also be noted that the majority of the series was set in pre-2000 and while I wouldn't say that our technology was terrible at the time, we have come a long way since then. For all we know, the epilogue could be taking place in a world where magic has been exposed to the muggles and both sides are living in harmony.

I know, extremely unlikely but it would make for a hell of a fanfiction to explain those 19 years.