The mystery continues, just got a reference tested lamp from my dealer. Unfortunately it was a 50W lamp and my DC power supply can only get it up to 12.4 volts then (I bought 35W lamps), and it became 3700K at that voltage.
Getting paranoid, I made visual comparison with a Grafilite Mode A3 fluorescent which others than me has measured to ~5500-5600K (I get the same result), and clearly the light from that is bluer.
I also did the white balance picker thing, with high CRI sources color temp can be guess quite well by the camera and indeed it shows almost exactly the same values as I measure (a little varmer as the paper is not 100% white).
The other picture attached with the brighter lamp is the 35W run at 16.4 volts, and then I get 4700-4800K, but voltage is way too high for that.
It doesn't seem likely that the measurements are wrong, considering both methods showing the same thing, and other lamp measurements matching other people results.
So I need to try with a different power source and see if I get some other result, there still could be some issue with my DC power supply. I have measured it, but only the voltage, maybe it does something funky when delivering power...