One rule the courts generally follow is that they try to limit the scope of their rulings. Plus, of course, the country is divided into several federal districts, and a ruling in one district doesn't necessarily apply to other districts. So I understood the injunction out of a San Francisco courtroom only applied to particular travelers whom, via the ACLU, had filed a challenge to how the order was applied to them. The injunction does not apply to other travelers, other federal districts, or people who are affected by the order for other reasons.
I understand the DHS statement to simply amount to "we aren't lawyers, so until a judge rules on whether the entire order is constitutional, we have to assume it is and act accordingly. We have lawyers on staff who will tell us how other rulings affect our actions, and how far those rulings go."
It's important to remember that executive orders are legally binding on people who work for the president, but not anyone else. Usually, they say how an ambiguous law will be interpreted, or they add limitations on top of what the law requires.
In this case, the president has directed various people to take certain actions. The courts will have to determine if those actions are legal. It wouldn't surprise me if some actions are legal (cabinet members are supposed to review the policies for the refugee program) and others aren't (prioritize immigrants based on their religion). But DHS doesn't get to conduct its own review of the order; they have to assume the whole thing is legally binding.
If multiple federal courts start granting injunctions against particular parts of the order, then things might change. I'm not sure how that works; although I am sure that government-paid lawyers will conduct their own review of the order, and I strongly suspect that the president has to approve any decisions to not implement a portion of an executive order.