My friend have this issue with his GS3 and can confirm it's a Samsung problem.
You can enable both WiFi and Bluetooth at the same time. However when you do WiFi will not work. I don't think Samsung understands radios very well. I've seen this done with many other phones without problem. has has sent their tech support an email about this today and hopefully there is something that can be done. has has also asked if this is an issue on the Galaxy S4, if it is I may consider the HTC One after all.