The Boston mayor pleads ignorance of the inconvenient facts.
But the Atlantic reported at the time of the bombing here:
At some point within their first year of being here, the family would have had to apply for asylum. (If they'd already outstayed their six-month visa, they could have applied defensively if the government was trying to deport them.) Asylum-seekers, like those seeking refugee status, must demonstrate that they have a "well-founded fear" of persecution in their home countries. This is a necessarily subjective determination for the government to make, one that has been subject to various legal decisions over the years. (For those curious: Asylum seekers apply for refugee status from within the U.S.; refugees seek it from their home countries.) ... After a year of holding status as asylum seekers, the family would be eligible to apply for green cards. Again, a security check, which by now would include reviews of the entire immigration application history to ensure that there was no apparent fraud. In 2007, Dzhokhar Tsarnaev — the younger brother, suspect 2 — received this status. Despite early reports, his brother Tamerlan apparently never did. At some point, he returned to Russia to renew his passport, according to his father.