This is a complete misrepresentation of what Quakers believe and what it means to be a Quaker.
This is what George Fox actually said:
“Be patterns, be examples in all countries, places, islands, nations wherever you come; that your carriage and life may preach among all sorts of people, and to them; then you will come to walk cheerfully over the world, answering that of God in everyone; whereby in them you may be a blessing, and make the witness of God in them to bless you.”What this says is that if you act in a certain way in the world – 'your carriage and life' - then you will experience something which will feel to you as a 'blessing' which will be reciprocated back to you by those you meet. It is this that George Fox describes as 'that of God in everyone'. It is not a belief but a way of describing the felt response in our hearts as a result of the way we act in the world. It is not a call to believe, but a call to action in the world in a certain way – 'be patterns, be examples'.
What Quakers do believe is that if we are to have any integrity at all then we must discover the truth in our hearts and minds for ourselves, and that the way that we do this is to come together in the gathered meeting and wait expectantly in silence. If we bring all our troubles and concerns, our joys and sorrows, to the place of silent waiting in our community, then we believe that the truth of our lives will be revealed, our 'condition' will be spoken to, as George Fox puts it - with both comfort and discomfort.
The truth that we discover and share in the gathered meeting will then be confirmed by the best of the teachings of scriptures and the words of the sages down the ages, but confirmed directly in the world as it is for us today.
The gathered meeting is not a refuge from the world where we can contemplate 'that of god in everyone' to our hearts content, but rather a place of discovery, where the truth of our lives is revealed and where we discover that which we must do in the world.
The 'promptings of love and truth in our hearts' that come to us in silent waiting are calls to action with integrity which will result in us 'walking cheerfully over the world' no matter what may befall us. The rest – peace, equality, simplicity, community, follow from this.