Analysis:
JOIN::optimize performs constant optimization of GROUP by clauses
by calling remove_const():
    group_list= remove_const(this, (old_group_list= group_list), conds,
                             rollup.state == ROLLUP::STATE_NONE,
			     &simple_group);
If it turns out that a GROUP clause references a field that is
computed by a single-row subquery, then the said optimization
performs premature execution of the subquery referenced by the
group clause.

Solution:
Block the evaluation of subqueries similarly to the approach
for the WHERE and JOIN..ON clauses.