What the author is saying in a rather obtuse way is a reflection of the provisions of IAS 21. Asset and liability items are translated using a closing rate as of the balance sheet date - here, the middle rate as of the balance sheet closing date/reporting date. Income and expense items are translated using exchange rates as of the transaction date. Here, "using transaction date exchange rates that are approximated by annual average rates".
http://www.iasplus.com/en/standards/ias/ias21And of course, I agree with Robin B. :-)
One last note: When asking questions about accounting, please ALWAYS indicate which accounting standards are involved - HGB, IFRS, FER. It does make a big difference - esp. for German terms that are the same in German but different in English - je nach dem Standard.