This is true regardless of whether someone believes in God or whether God exists.
So what's your point?
Hopefully I can make it a bit more clearer by saying this: If a theist for example, seeks to do away with the objective moral standards and values which they affirm as being prescribed by God, and plug in his or her own values and morals (whatever they might be), he is acting
in willfull contradiction to the prescribed objective moral standard. In other words, the objective moral standard still makes a claim upon the person, they just refuse to adhere to it.
On the other hand: when one who does not believe in God denies the existence of objective moral standards and plugs in his or her own values and standards, they are acting
in accordance with their view of life. When he or she rejects the belief in God, then someone (the individual themself) has to become the prescriber of some set of morals and standards, however noble or base these standards might be.
Because a moral law or standard is a
prescription and prescriptions come only from
prescribers. For example, unlike the laws of nature (which are only descriptive), moral laws are prescriptive. Moral laws do not describe what
is; but they prescribe what
ought to be. They are not simply a description of the way people
do behave, but are imperatives as to how they
should behave.
I hope this clears things up a wee bit.