Like said, it is just one sign that it can be compatible. If you want it to know 100%, you will have to try it yourself and with all BIOS versions and all motherboards on the market.
It´s like always, new hardware should work on old standardized hardware connections, but still some software/firmware/BIOS will not recognize it or will recognize it correctly with no issues.
HP will tell you that it should work, but it´s not designed to work with other hardware than sold with this system from HP.
Motherboards sold seperately have better support than prebuilt systems like your HP, but even than it´s up to the manufacturer to implement a future proof BIOS or release new updates for it.
You will have to look into your specfic motherboard and search over the net for a compatible graphics cards with this board.
as far as I found:
The 750TI, 660TI, R9 280, HD7790 should work
an incomplete list of compatible graphics cards can be found here:
http://www.userbenchmark.com/System/HP-Elite-7300-Series-MT/2247
RX 460, gtx 960, 970, 1050ti, 1060 not:
https://forum-en.msi.com/index.php?topic=278498.0
https://www.reddit.com/r/pcgamingtechsupport/comments/5h4sba/pc_wont_work_with_new_msi_gtx_1050_ti_4gb_gpu/
https://forums.evga.com/EVGA-GeForce-GTX-970-Boot-up-Beeps-m2319286.aspx
https://forums.evga.com/m/tm.aspx?m=2318143&fp=5
https://www.reddit.com/r/buildapc/comments/5snw44/bought_gpu_incompatible_with_mobo_new_mobo/