Actually, Olivier, you're completely wrong about that, because there's a bug in your sample code. It will indeed return $row['MAX(time)'] - you have to pass the MySQL resource to mysql_fetch_assoc() and you're not doing that. This:
$row = mysql_fetch_assoc($conn)
...where $conn is your DB connection, would in fact produce a result. The complete example below is taken from my own self-written content management system:
$query = 'SELECT MAX(ctRevDate) FROM content group by ctPage';
$querySet = mysql_query($query, $conn);
$row = mysql_fetch_assoc($querySet);
print_r($row);
This produces:
Array
(
[MAX(ctRevDate)] => 2004-01-15
)
..on my testbed. So it doesn't in fact need an alias at all.