Personally - I have to side with Washington on this one. Not to raise the alarms here, but I can think of 19 guys not all that long ago who came to this country legally, and at one point would have passed a simple background check. 19 guys who are PRECISELY the people we do NOT want to have guns on our soil.
I absolutely do not want to minimize the tragedy of 9-11, but the statement above is, by definition, prejudice. "Pre-judging" ALL legal aliens by the actions of 19 aliens who may or may not have been legal is not a reasonable comparison, especially when you use it to apply the addition or subtraction of rights. If we follow the logic above, then US Citizens should not have guns because more people were killed in any given year by US Citizens than anyone else (including 2001). From there, we can start slicing and dicing the right to carry a gun by race and sex "these people get them and those others over there don't". You can see where it leads...
I did some very quick research and the data I found don't seem to support the theory that legal aliens have more of a propensity for crime than native US Citizens.
"In fact, the incarceration rate of the US born (3.51 percent) was four times the rate of the foreign born (0.86 percent)."
the quote above is here http://www.migrationinformation.org/Feature/display.cfm?id=403
FBI reports "Law enforcement agencies submitted SHRs to the FBI for 14,831 murder victims who were slain in 2007". I would guess that at least the majority of these were committed by US Citizens.
http://www.fbi.gov/ucr/cius2007/offenses/expanded_information/homicide.html