Farnborough provide the lower airspace radar service for Odiham and there will have been discussion between the respective ATCOs before your MATZ crossing was approved. This MATZ crossing approval will have contained a height restriction and presumably you gave an intended track. If your clearance was for below 2000' and your track took you within 2.5 NM of the centre point of the longest runway (1850m+) then I believe that you also had permission to penetrate the ATZ. When a MATZ has been active I have never heard of a military ATCO giving an additional clearance specifically for the ATZ.
However I cannot fault the statement 'if in doubt ask'
