Nonsense. It only says that habeas corpus cannot be suspended except when in cases of rebellion or invasion the public safety requires it. Nowhere does it specifically say that only congress can suspend it. And nowhere does it say that it requires an act of legislature to do it.
The constitution specifically says in the article containing the habeas corpus power that "All legislative Powers herein granted shall be vested in a Congress of the United States." That means Congress and Congress alone may suspend it.
So exactly what is it about the phrase "shall be vested in a Congress of the United States" that you do not understand, non-seq?