Well after a year, I have solved my frustration. I figured out that HP was just using sharing to access the printer and the card became a drive on that share. Below is how I now mount my card without running the HP software.
Mounting SD Cards on HP Photosmart All-In-One Printers
1. Put card in appropriate slot on printer.
2. From Finder choose Go > Connect to Server.
3. Enter smb://
4. Press Connect.
5. When prompted for user name and password select Guest and press Connect.
At this point, your printer should be added as a share and if you are lucky iPhoto will auto start.