Mosqueda, 51, cleared an FBI criminal history check and an intelligence review from the US Transportation Security Administration.
The TSA said the checks aren't designed to identify people with Mosqueda's type of record, which includes a two-year prison term for a 1996 heroin conviction and other arrests but no terror charges.
"We're looking for terrorists," spokeswoman Andrea McCauley said Tuesday. "We're looking for people who would be involved in terrorist activities -- that's the scope."
On Tuesday, demolition crews finished clearing the charred debris, and hundreds of thousands of commuters settled into taking public transportation to their jobs -- unless they could work from home.
It was clear the highway collapse was impeding traffic, but rush-hour slowdowns didn't turn into the gridlock authorities had feared.
The cleanup has cost taxpayers $8.8 million so far, including $2.5 million for one day of free passage on subways, buses, and ferries for commuters, state transportation officials said.
Investigators said Mosqueda may have been speeding at the time of the crash, but do not believe drugs or alcohol were factors in the accident.
Joe Come, program director for motorcarrier safety for the US Department of Transportation Inspector General's Office, said the crash raises a broader issue.
"There's a general question of how hard do you want to make it for people to get a commercial driver's license or anything else that can affect public safety," Come said.
"Do we hold them to the same standard as airline pilots?"
Family and friends said Mosqueda, who remains hospitalized with second-degree burns, has been sober for a decade, is active in his church, and works as a drug and alcohol counselor with a Hispanic health organization.
But an industry specialist questioned rules that allowed someone with Mosqueda's background to operate a truck loaded with more than 8,000 gallons of gasoline.
"He is unemployable because of [his] past record. That would be our recommendation right off the bat," said Darryl Tolentino, managing director of Fleetwatch Systems Inc., which performs driver background checks for trucking companies.