Germany is counting deaths differently. If you have heart issues and you die due to a heart attack you're not counted as a COVID death. In Italy you are as long as you test positive.
That doesn't seem to be the case - a man from Baden-Württemberg, who died earlier this month, was only tested positive AFTER he was already dead for a few days and counted towards the statistic.
This means your general statement cannot be true.
EDIT: I do not mean to imply that Italy failed in any respect. Italy has one of the best HC systems in the world.
The only reason this testing aspect worked out well for Germany is a very localized testing system. This type of 'federalism' is now a big issue though, as the gov can't simply ban events - only the states and communes can.