My response to you statement is this:
I cannot respond to the question until the person defines the word "God". The reason for my response is that God means many different things, and is interpreted differently by many people. For instance: God is viewed very differently by a Hindu and a Scientologist. To one person, the idea of God may be very exclusive. To another, God may be all inclusive. The word has been assigned hundreds of meanings. It can mean something all important that a person lavishes attention on, such as: "his work became his God". It can mean a mythological personage, a Holy Trinity, a state of enlightenment, the collective unconscious, unconditional love, an omnipresent being, and so on.
Even if we narrow the definition to mean a higher, unseen power, the statement still is not necessarily true. Most people can conceive of a higher intelligence, or a mind with greater awareness. Are those things illogical? I don't think we can assume that a believer in God lacks critical thinking. Some people might say that we cannot prove God exists. But I would also argue that we cannot irrefutably prove that God does not exist.
There are many things humans can't sense because of the limited range of their abilities. We cannot sense radio or television waves as they are transmitted through the air. We cannot see objects in different spectra of light (like ultraviolet) or objects that are too tiny or distant. We cannot hear noises out of our range of hearing. Yet, they exist. We have found ways to prove their existence, but our ability to do so has only been recent. We could not prove the existence of some of these things as recently as two or three centuries ago. Does that make their existence any less valid?
Perhaps in our present state of evolution, we cannot irrefutably and scientifically prove the existence of God. But if you use the logic behind the arguments I just gave, it does not mean that God does not exist. Therefore, I would say that the person who made the statement has shown his own lack of critical thinking. Furthermore, he or she has made a rather discriminatory accusation by assuming all people perceive God in the same way.