The documentation should probably change from "True when Min is the smallest member..." to "True when Min can be unified with the smallest member...".

?- min_member(3, [1,2,X]).
X = 3.

Or document this behavior explicitly?

See here for a discussion on SO.

See also

• max_member/2 (with comments)
• min_list/2
• max_list/2 (with comments)

This is a general property of predicates that depend on the standard of terms which defines the order of all terms, including variables. Here is another nice one:

?- sort([X,2], [3,2]).
X = 3.

Also added comment on SO.