At least you recognize the true problem here. Let me help you out.
It seems that you have gotten somewhat confused, and are mixing not only arguments, but terminology as well.
First of all, we're discussing the terrorists who attacked WTC, the Pentagon, and were foiled in one more attack by a bunch of everyday heroes who "rolled" into history, not about Mexicans, keep your metaphors straight.
Next, let's define immigration for you:
Main Entry: im.mi.grate
Pronunciation: 'i-m&-"grAt
Function: verb
Etymology: Latin immigratus, past participle of immigrare to remove, go in, from in- + migrare to migrate
Date: circa 1623
Inflected Form(s): -grat.ed; -grat.ing
intransitive senses : to enter and usually become established; especially : to come into a country of which one is not a native for permanent residence
transitive senses : to bring in or send as immigrants
- im.mi.gra.tion /"i-m&-'grA-sh&n/ noun
- im.mi.gra.tion.al /-shn&l, -sh&-n[^&]l/ adjective
These murderers did not enter this country under the pretense of migrating here, they came in on visas issued to people who come here on business, for schooling, or as tourists. Legitimate visas, issued by our consulate or embassy (part of the State Department) in their country of origin, not "La Migra".
They got past Customs (an agency of the Treasury Department) at their point of entry because their papers were in order.
Then they applied to the INS (part of the Department of Justice) for a visa extension, or a change of status.
The INS, not having access to CIA and/or the FBI intelligence ref: the classification of some of these people as terrorists, granted the visas based on lack of negative information.
The real problem here is the decentralization of the system, this is what allowed the terrorists to get in.
What we need is a new agency co-ordinating the functions of these separate entities, and forcing the sharing and effective disbursement of information.
Come to think of it, Bush just created that agency, didn't he?
Let me know if you need further help.