Aluminum reacts vigorously with water in very basic solutions.

The assumption is that the aluminum is reacting with sodium hydroxide. That isn't quite the case.
Aluminum metal always has a passivating layer of aluminum oxide on the surface. Before aluminum
can react, the protective layer must be removed. Al2O3 dissolves in concentrated base, and this
exposes the aluminum metal to water with which it reacts much like the alkaline earth metals do
to form aluminum hydroxide and hydrogen gas.

Removal of passivating layer:
Al2O3(s) + 2OH- + 3H2O --> 2[Al(OH)4]-

Reaction of aluminum metal and water:
2Al(s) + 6H2O(l) --> 2Al(OH)3(s) + 3H2(g)

With an excess of hydroxide ion, the solid aluminum hydroxide will dissolve to form [Al(OH)4]- in solution.
The aluminum hydroxide precipitate will disappear.
Al(OH)3(s) + OH- --> [Al(OH)4]-

This is why there a small pieces of aluminum foil in some drain cleaners. Drano is solid flakes of NaOH with
small pieces of aluminum foil. As the aluminum foil reacts, hydrogen gas is liberated which tends to "stir the pot",
and agitate the mixture to more readily dissolve the hair clog. Sodium hydroxide is used because the hair that
forms most clogs will dissolve in basic solutions.