I'm trying to work out the logic here.
Representatives of various industries that employ large numbers of immigrant workers (food service and hotels, retail, agriculture and food processing) have formed a group to lobby for regulations that would allow guest workers into the country on a limited basis tied to their employment. These workers are "essential," the group says, because they're needed for jobs American citizens won't take. But these groups don't want regulations mandating a higher minimum wage - even though you'd think a higher wage might entice citizen workers to take those jobs - because, you see, "the market determines wages" (this is from a director of the American Meat Institute).
So: government action that mandates a minimum wage, that's "interference." Government action that creates a whole new class of worker - workers who, from desperation and powerlessness imposed by their guest-worker status (nearly similar to that of indentured servants), drive down everyone's wages...well, that's not interference at all.
It follows that "the market" includes industrial groups lobbying government on behalf of their interests, but it does not include labor groups lobbying government on behalf of their interests. Apparently the famed invisible hand is "invisible" only from the wrong side of a sort of two-way economic mirror: from that side, nothing can be seen but the reflection of one's fruitless efforts to have one's interests recognized; from the other side, the hand is visible indeed, and in full control of industry, who use it to steer profits and benefits exclusively their way.
(On the larger issue: the path to citizenship should be much simpler, and if NAFTA and the like allow capital to flow freely across borders, then workers should be able to move just as freely in search of better wages.)