I went back to verify the details on this particular question.
In fact, not only was Russia's PARTIAL MOBILIZATION against AUSTRIA recognized as NON-THREATENING by the Germans, it was OFFICIALLY PRE-APPROVED by the German Foreign Minister Jagow, on July 27 (reference: Fromkin page 224).
To understand what happened next, we must first know that the Germans only had ONE real set of war plans, the so-called Schlieffen Plan. That plan required Germany to FIRST invade through NEUTRAL Belgium, defeat France and THEN turn it's armies against Russia.
But German leaders, like Army chief Moltke also understood: before they could launch into NEUTRAL Belgium, they must first convince the world, and especially the German population (!), that everything was RUSSIA'S FAULT.
So, after Russia began its pre-approved partial mobilization against Austria, the German Kaiser turned on the Russian Czar, demanding he immediately de-mobilize, and when the Czar refused, Germany instantly declared war.
Then, as the Schlieffen Plan required, Germany launched it's war against RUSSIA by invading NEUTRAL BELGIUM!
But of course! How would you do it?
Invade Russia?
;OD