Hi Jb
There's one very good reason for the 'secretive' behaviour which you've
omitted to mention and that is propensity of governments to declare war
against another nation, especially if the perceived enemy was yours or your
(grand)parents homeland.
Hello Rena
Valid point that I should have included indeed. Only keep in mind that that great granduncle of mine, the one I mentioned earlier, was quite proud of the military service he provided the Fatherland as a German officer. He even brought his old uniform with him to the states from his days in the Bismarck wars. Having lived through WWI, by then a US citizen of more than 50 years, he had no qualms, even to his dying days, of spinning up German military marches on one of those early Victrolas for his young grandson, so that they could march around their parlor being two little Kriegmeisters (that is, until his wife appeared and chased them out of the house).
And then there's my great grandfather, who had just become a young doctor in Hannover when certain events forced him out of Germany and into California. He immediately took up his petition papers for American citizenship upon his arrival, but also returned to Germany only 3 years later to serve as a surgeon in the Franco-Prussian war. Makes for an off the wall scenario to say the least, but I personally (and thoroughly) documented this some 25 years or so ago. So while I'll concede many must have felt guilt (or even a bit of shame) for their prior alignment to Germany, Prussia or the Reich, especially when their new and adopted country was taking arms up against them, others clearly did not (at least appreciably so). But what you mention remains a valid point, and certainly applied to many, perhaps even most.
Now to also play a bit of devil's advocate for a moment, I called the war in Iraq a crock and farce the moment it went down early in 2003, when we went from chasing the Taliban and Al Qaeda in Afghanistan (which this country fully supported) to running a holy crusade to de-claw Israel's enemies in the region. The stand I took was against popular sentiment at the time, but look where we are today, even if the federal government tells me otherwise. I suspect many Americans of German ancestry didn't buy into their cousins back in Deutschland being depicted by the press and government as "Huns" in WWI. I don't even buy into much of the same when it comes to WWII, and I've specialized in that study. But that's my own personal assessment, it concerns me little who sees it that way or not, to include what the media spouts off. But whenever it comes to "your government says ..." I IMMEDIATELY am on my guard. I've learned better, now that I'm all grown up and have learned to think for myself.
It may not have occurred to you that there is
another reason and that is when the inhabitants of a country believe that
their governments have allowed too many immigrants too much leeway to
practice customs from their old homeland. History shows that gangs would
come into a neighbourhood smashing anything that was alien, be it religious
or of 'foreign' ethnicity. At the height of these disturbances what parent
or grandparent is going to relate family history to a child born in the new
homeland when silence is the better option?
Well perhaps, only when were the Germans in America (or England for that matter) ever allowed "too much leeway"? The only vandalism or attacks I can recall were localized ones (and random and sporadic at best), normally small disturbances during times of war against Germany. I think any reservations felt by the elders at the time came less from the potential of marauding gangs and more from government sponsored propaganda. After all, it's always easier to go after your "enemies" once you paint them as devils. And by extension, the acorn doesn't fall far from the tree.
Also not to crash the party on this last point but have you seen how many illegal Mexicans now inhabit the US? Some areas in the southwest now resemble Mexico as much as they do the USA. Lots and lots of leeway has been given, with an incredible amount of tolerance from both the government (by design) and American citizenry (by default). So to follow your logic, where are all these American gangs that should be entering those neighborhoods smashing everything that is alien? Perhaps this would occur in Mexico if so many Americans were to invade there en masse, but obviously not in the good ol' USA - not anymore anyways. Remember that British rock song "Comfortably numb" I posted sometime earlier? It applies in so many ways.
But ok your point is taken. I'll give you both of those. Always like hearing your take on things. But we won the war. Against Howe and Burgoyne. 
Merry Xmas in England. I'll be bathing in the SoCal sun (bah).
Jb