MySQL: JOIN empty tables with a constant value column, COUNT(*) returns a 0, but adding a GROUP BY on the constant value returns nothing?
It does not matter what you group by, try for example TableA.id. The reason is that MAX and COUNT returns a scalar even for the empty set (your first query). If you add a group by (no matter what attribute you use), you get one scalar per group. But since there are no groups, you get an empty set.

It may be illustrative to add an outer query that count from your second query:

SELECT COUNT(*) 
FROM (
    SELECT 'Combined', COUNT(*), MAX(Timestamp)
    FROM TableA
    JOIN TableB USING (Id)
    GROUP BY 1
) AS T