I think they got their own internet that gets monitored.
They don't really have their own internet persay, they just don't have uncontrolled access to the internet at large. At least, not generally. I have a few Iranian friends, whenever they go home for extended periods it's not like we have to exchange letters. For some time they couldn't access Facebook at all but I would I still see mail from their gmail and yahoo accounts. There are a couple that manage to maintain broad access to the internet while in the country but from what I understand they have to go to extraordinary lengths to do so.
Much like all countries, don't confuse the citizens with the government as a whole. There is a tremendous divide in that country that did not just magically appear in February and then just as magically disappear in March.