I can only speak for the UK not FRA.
If the intersection concerned is considered by ATC and notified as a "same departure point" for vortex wake, then the 3 minutes can be reduced to 2, but only if you accept it. The intescection would need to be less than (approx) 400m from the full length departure point.
I bet getting you off the runway wasted more time than waitng the extra minute!
It is good ATC practice to ask if you can accept the reduction in time prior to issuing a line up clearance.
If it wasn't an intersection notified for this reduction, then ATC were wrong and you were right.