Can I buy a card without any treasure cards on my hand?
Short answer: yes, its possible and it has been officially acknowledged that the German rules are wrong.
Long answer: as you have already quoted from the base game rules (emphasis mine)

The cost of a card is in its lower left corner. The player may play some or all of the Treasure cards from his hand to his play area and add to their value the coins provided by Action cards played this turn.

Your total available money comes from played treasures and action cards.
An additional example for a leftover buy:

If he wants to use all 6 coins to buy one card, he can buy a Copper (for free) with his second Buy or not buy a second card. Players do not have to use any or all of their Buys.

This example makes clear that you can buy cards for free, thus you are not required to play any treasure cards.
The English rules are the original ones and take precedence over any translation. Furthermore, Hans im Glück, the German Publisher, have officially - and indirectly - acknowledged that this phrase in the rules is wrong. From their &quot;Regelfragen&quot; Rules Questions page

Kauf
Zitat aus der Regel: &quot;Um eine Karte zu kaufen, legt der Spieler eine der mehrere Geldkarten aus seiner Hand offen auf dem Tisch aus. Zu diesen Geldkarten kann er das virtuelle Geld auf seinen zuvor usgelegten Aktionskarten hinzu zählen.&quot;
Dies bedeutet nicht, dass es nötig ist Geldkarten auszulegen um die Boni durch virtuelles Geld nutzen zu können. Es können auch Käufe ohne eine einzige ausgelegte Geldkarte durchgeführt werden.
Karten die 0 Kosten, können immer gekauft werden, solange der dafür nötige &quot;Kauf&quot; vorhanden ist.

Which roughly translates to:

This does not mean that Treasure Cards must be played in order to be able to use the virtual money. Purchases without playing any Treasure Cards may be carried out in this way.