Why would you not want to believe the numbers quoted by Gulfstream??.
Do you think that they would lie?.
Do you think that if they did lie that pilots and operators would not have publicised that lie?
There are enough of them flying worldwide now now that it should be easily verified.
Go to Flightaware, find a G650 or two and track their flight history, it should be fairly easily determined what their range is.
Gulfstream are well known to be very accurate in their actual claims.