It isn't altruism or Christian charity or the desire to treat all men equally that fuels big business' backing of open immigration policies. Businessmen admit this in whispers among themselves all the time, and every now and then one of them lets it slip in public. Once in a great while one even has the -- I don't know if the word is 'audacity' or 'foolishness' - to propose a policy which makes this impossible to ignore.
I'll add that it isn't just the price-point of wages which incents business to support as much open immigration of unskilled labor as possible. It isn't as though there isn't enough unskilled labor right here, in the form of our own countrymen. It is just that in addition to being relatively more expensive than immigrant labor in terms of direct wages, these countrymen of ours are also - though one has to be delicate in how one says this, ironically in order to avoid a charge of racism for having the audacity to consider the possibility that our own countrymen are employable even though they are not white - objectively more difficult to employ, leading to greater expense and uncertainty, two things which American capitalism is designed to ruthlessly minimize.
I'll emphasize, though, that this latter labor pool consists of those who are already our neighbors and countrymen, to whom as an objective matter we have a greater obligation than we do to men from other lands. "Jobs that Americans won't do" is at least in part code for "jobs it is easier and less expensive to hire unskilled immigrants to do than it is to hire inner city Blacks to do". (Oddly, the Time article misses the elephant in the room entirely).
Business isn't the only faction in favor of open immigration, of course, though without business as bedfellow it seems unlikely that the push for ever more open immigration would be politically practical. And I'm sure plenty of businessmen tell themselves bedtime stories about family values and the Rio Grande. But don't kid yourself about what is fueling the boilers in the engine room, and don't kid yourself that you have no indigent countrymen who are harmed by the wedge that more pliable and easily employable immigrant labor drives between these countrymen of yours and escape from conditions which make Dickens look like a peaceful oasis.