Unfortunately, that information is correct, post office workers should not postmark anything smaller than a large letter.
I have had a same problem with many of the post offices that I have visited on search of stamps.
Really though its is at the counter staffs discretion. Some will do it no questions asked, most will not do it, unless you send the postcard as a registered letter (ppffftt No Way!)
Some will even insist you buy some stamps or will only cancel the stamps sold from that post office.
Fortunately I have kept my local Post Office team sweet, as I tend the purchase alot of stamps from them (they stock specials and themed stamps) and mail out personal and work mail, and occasionally purchase currency.
So they tend to postmark my postcards at the point of posting, but I know when not to take the *Ps***
Lately dispite handstamping at the counter, my postcards and letters have been machine cancelled over the top and some occasions pen/markerpen cancelled dispite the post office cancel. 
So No guarantee of a good cancels