More than likely it is the same thing that is wrong with the DHT11 sensor. Re: DHT11 Temperature Sensor Issue
The speed of Galileo's I/O pins are just not fast enough to keep up. The DHT11 needs a response time of 80us, (https://www.sparkfun.com/datasheets/Sensors/Temperature/SEN-09570-datasheet-3901090614M005.pdf) using fast I/O Galileo can get to 50us toggling, but if you need to do calculations between the signals, it will not work.
It looks like the RHT03 requires a response time of 80 us. (http://dlnmh9ip6v2uc.cloudfront.net/datasheets/Sensors/Weather/RHT03.pdf) The Galileo just cannot go that fast.
You can plug your sensor into an Arduino, just to double check that it is not a problem with the sensor.