What happens if you use a sub query to get the minimum value for each partition, and then get the min of that?

i.e. Something like this:

SELECT MIN(MinIntDate)

FROM (SELECT PartitionID, MIN(IntDate) MinIntDate

FROM dbo.ExampleTablePartitioned

GROUP BY PartitionID) a

or

SELECT MIN(MinIntDate)

FROM (SELECT PartitionID FROM dbo.ExampleTable GROUP BY PartitionID) a

CROSS APPLY (SELECT MIN(IntDate) MinIntDate

FROM dbo.ExampleTable b

WHERE B.PartitionID = a.PartitionID) c