The Palestinian passport is not recognized everywhere but it is better than nothing, and it seems that the PA has a deliberate policy to deny many Gazans the ability to obtain one that they could use to travel through the Rafah crossing, or when they get permission to go through Israel. Egypt has recognized these passports in the past.
While Israel apparently has to give permission as well for Palestinian passports (according to Wikipedia, although the page seems dated) this NGO is not blaming Israel but the PA. If Israel was stopping the issuance of passports, you can be sure that it would be making headlines.
Gisha, the Israeli NGO that supposedly deals with freedom of movement for Palestinians, has nothing on this topic.