You need to be more specific in your question, if you want a more specific answer. The question could be read in a number of different ways.
When you say immigrant do you mean American who immigrated and became an American, political refuge who was gifted citizenship, foreigner here on a student visa looking for part time work over the summer, someone with a foreign accent looking for a small contract job like building your backyard deck, American with non-white skin color, H1B visa worker from India, Chinese citizen temporarily here on work or student visa, or someone you know to be an illegal Mexican immigrant? Which one?
You say discounting the value of training is evidence of a lack of balls. I say what training are you talking about and for what job? If I have two software engineer candidates in front of me who will be working on a two year project that uses a particular type of data base, I'm taking the better engineer not the one with specific experience in that database as I know how that the amount of time it takes to get accustomed with a database is negligible for a good engineer. In my experience the delta between top notch engineers out weighs specific experience by an order of magnitude.
That said if I'm looking for systems engineer I'm not gonna hire an IT guy who thinks it would be cool to learn to be a systems engineer, as I know it will take many years to train the IT guy to be an Systems Engineer even if he has the aptitude.
If that IT guy wants to become an Engineer he can take out a loan and get the education.
You see, your question was not specific enough to answer. Could I come up with a scenario where there is a choice between an American and an Immigrant, and not a choice between two Engineers, .... I suppose I could but you have not done that.
I avoided industry- or sector-specifics for exactly this reason; preferring to paint with a broader brush and to serve-up a generic choice between investing a bit of money in the (re-)training of an American worker, versus choosing an immigrant that has already undergone the training.
But, fine, I should be able to drill-down sufficiently to help us facilitate this choice, without over-reaching or annoying either of us...
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SCENARIO:
01. This is May 2014.
02. Your long-range project schedule indicates a need for a worker in 6 months.
03. Entry-level software developer.
04. MCSD certification or equivalent combination of training and experience.
05. Coursework emphasis on:
a. .Net 4.x.
b. Visual Studio 2012
c. M$-SQL Server
d. C#
e. IP networking
f. M$-Server 2012 Enterprise
06. Two extremely high-caliber candidates present themselves.
a. an American citizen.
b. a foreign national looking to immigrate, and willing to pay his own way here.
c. Your search is over; you want one of these two; nobody else would be better.
07. Neither have any prior skillset-specific work experience.
08. Both place well re: communications, personality, intellect, perceived work-ethic, etc.
09. Both want (and expect) the same starting salary and benefits.
10. Both are in school, due to graduate with your needed skills, 5-1/2 months from now.
a. the American via a domestic trade/tech school; funded by taxpayer retraining dollars
b. the foreigner via an overseas trade/tech school; funding source is immaterial
11. Your choice is:
a. the American worker; taking advantage of the outcome achieved via those
taxpayer dollars; with the added bonus of taking him-or-her off of welfare.
b. the foreign worker; taking advantage of his education through means other
than that provided by US tax dollars; sponsoring him as he enters the US;
with him reimbursing you for any outlay or administrative costs; zero-sum.
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Hopefully, that is specific enough for your purposes.
If not, feel free to continue tweaking the model until it yields something that you think would be agreeable to the two of us, in pursuit of that 'straight answer'.