It looks like the sort of bug where the parser designers never tested a correlated 
derived table in a select list used with aggregates. This should instead give you an error message, as derived tables consisting of correlated subqueries are generally not allowed. I think it's performing the correlation before aggregating, essentially overriding the aggregation of the first MIN(). Your first formulation is better, anyway, and you could also (as you like derived tables 
) try:
SELECT c.defendant_sid,
count(*) as [count],
CAST(MIN(c.calendar_time) as char(20)) as [MIN(calendar_time)],
CAST(x.xMin) as char(20)) as [Min2]
FROM #temp c JOIN
(SELECT Defendent_SId, MIN(Calendar_Time) xMin
FROM #temp
GROUP BY Defendant_SId) x ON x.Defendant_SId = c.Defendant_SId
WHERE c.defendant_sid < 10
GROUP BY c.defendant_sid, x.xMin
ORDER BY c.defendant_sid
--Jonathan