I know the controllers were busy at that moment and that's why refused my
clearance. Why didn't they just issue a sqawk code with the instructions
"remain vfr"? Does it have to do with the nearby ADIZ?

My guess is yes. They also could tell you to stand by while looking
for it. During a time between 9/11 and the introduction of the ADIZ,
I was able to pick up my clearance while airborne from BayBridge (W29)
to Frederick (FDK) while circling over the bay. It took the
controller a couple of minutes, but once she found it, everyting went
fine.

That was a big hassle you went through, call FSS, call another FSS,
take off, get chewed-out twice, land, call Potomac, take off again,
....