It took me a couple of days to figure this out, but from some other discussions I have read here some people are still trying to figure this one out. I hope this helps those still having trouble.
I could not capture HDV into Premiere CS5. The capture window would say device offline and the record button was grayed out. However, DV worked fine. I went through the XH A1 menus over and over, and everything said HDV, including the front dial of the camera - HDV was lit, not DV. I searched through the web and was able to piece together the solution.
The XH A1 does not allow certain menu options when the firewire cable is connected to the camera. So, when I was seeing the DV downconvert option grayed out on the camera VCR/Play menu, I assumed that meant it was off, or unavailable. Wrong!
I turned off the camera and disconnected the firewire cable. I then turned the camera on to VCR/Play and opened the menu. The DV downconvert option was no longer grayed out; it was available and it was set to ON. I changed that to OFF, turned off the camera, reconnected, etc. I selected HDV 1080i and opened capture. It worked. I could capture HDV 1080i.
Of course. the blue screen appears in the capture window saying HDV is being captured - there is no real-time monitoring of HDV capture like there is in DV.
Bottom line: set the camera options before you connect the firewire cable. The DV downconvert is set to ON by default. Make sure it is set to OFF.