what is the difference?
You apply for the work permit.
If it either granted or not.
Obama has removed an obstaclewhy it would not be granted; - legitimacy of presence.
All things being equal and legitimacy being the only road block; Obama has allowed them to be given a work permit.
You are splitting hair on the verbiage - the intent is still there.
But all things aren't equal, which is the whole point. There are myriad reasons why people can be denied work permits. Saying Obama has granted people work permits is clearly, obviously false. Saying Obama has allowed people to apply for work permits is clearly, obviously correct. If every single person who applied got one you would be correct that it's just hair splitting, but that's not the case.
Regardless, it's beside the larger point that Obama is acting in the same manner as many previous presidents that have done so without any complaint. It's just political opposition desperately searching for a way to attack Obama on an extremely popular initiative. When you can't argue substance you argue process.