I rather suspect that this "I am not against immigration. I just want to control it." comment is a temporary attempt at avoiding the xenophobic,racists accusations.I don't want to end immmigration -no one does. I just want the sovereign ability to legislate it for ourselves. You may say "but if we want to remain in the common market we will have to accept free movement anyway", which may well be true, but I we do choose that then at least it is a choice, and we can unchoose it at any time if we see fit. Outside the EU we have the option.Maybe your fantasy that leaving the EU will end immigration is irrational.
What the Brexiters really mean is that they want to control all immigration so that, in the future, they can reduce it to practically nil by increasingly stricter controls and tolerances.
All of this "we can replace the desired skills from non-EU countries" is just an attempt to bat away the accusations.