Yes, this is part of the definition of a Mealy Machine. This is why people refer to the Synchronous Mealy machine as being a Moore machine; the output isn't dependent on the input, so they reason it must be a Moore machine.You write:
Are you 100% sure about this? I don't have contradicting examples, but I 'd like to see some proof.
http://en.wikipedia.org/wiki/Mealy_machine
http://en.wikipedia.org/wiki/Moore_machine
http://www.jflap.org/tutorial/mealy/mealyMachines.html
and since I don't want to just quote websites, here's a quote from Digital Design: Principles and Practices 3rd edition by John F Wakerly:
A sequential circuit whose output depends on both state and input as shown in Figure 7-35 is called a Mealy machine.(pg. 551)