You are not wrong, it probably should have said that. It does say we recommend JDK 8 on the store's download page, but it doesn't say the others wouldn't have worked.
However, we are actively addressing compatibility issues. If you click the like to the known issue you will see that it's ready for testing. Mango 3.4, the beta of which is released, can be launched on Java 9 without encountering that illegal access exception. There may be lingering issues yet undiscovered, but you can definitely use Java 9 now! I haven't tested JDK 10 with it.