You’re partly right, but there are actually a fairly significant amount of lateral transfers to other emirates (through the federal budget, which is mostly funded by Abu Dhabi). Things like the electricity and water system are run federally (by FEWA - the Federal Water & Electricity Authority) in 4 northern-most emirates. Many other benefit systems are also mostly funded by Abu Dhabi, and primarily for the benefit of the citizens of other emirates — one example might being the Sheikh Zayed Housing Programme. Abu Dhabi actually does help the nationals in all the emirates.