>>Did any NT Christian ever bad-mouth the Roman Government?
>Yes. The apostle Paul, at least, exposed a legal injustice perpetrated on him by Roman Government.
Requesting that an administrative error be corrected is bad-mouthing the government?
Yeah, Paul did not "request that an administrative error be corrected."
Act 16:37 But Paul said to them, "They have beaten us publicly, uncondemned, men who are Roman citizens, and have thrown us into prison; and do they now throw us out secretly? No! Let them come themselves and take us out."
Paul refused a direct order from a government official, and demanded an apology... YES, he bad mouthed an unjust government.