The information you're going to need to diagnose and work with this issue is going to be in the packages themselves (keep in mind these packages are from HP directly and not created by SolarWinds).
The rules in the packages for driver updates and most of the updates in the HP Business packages you're referring to contain WMI queries. My suggestion is to get a test machine and a test update to start with. Make sure you can process the query from the Patch Manager server to the remote client. If not, you need to investigate why:
Does the query run from the local machine? If yes, maybe the query is being lost in the network (routing, firewall, etc). If no, does HP have tools that are necessary to install the necessary name spaces for the WMI queries? Dell has similar tools in some situations, so if you're not even seeing the update as applicable then you may want to make sure the correct information is there.
If you're getting a different result than what is in the package, you may need to clone it and update the package rules to work for your environment.
For example, I reviewed this package:
NVIDIA Quadro Professional Driver Windows 7/8 (x64) [377.11.A1]
Under the Prerequisite rules it has rules for x64 architecture (make sure your test machine isn't x86) and the WMI query:
select * from Win32_ComputerSystem where (Manufacturer='Hewlett-Packard' and not (Model like '%Proliant%')) or (Manufacturer='HP')
Next, under the applicability rules there are dozens of rules that appear to relate to model numbers:
select * from Win32_BaseBoard where Product LIKE '%802f%'
You will need to make sure one of these evaluate otherwise the update won't be applicable and won't be presented to the machine.
If these are evaluating for your test machine then you may be looking at an issue elsewhere in the process: If it fails to install, what's the error? This specific update is an EXE, does the EXE install successfully when installed directly? Are there any other indicators or pieces of information you can provide from the process?
The answer may be in testing with the information provided above, but there could be other things going on. As other third party updates appear to be working I'm focusing on what's different for the HP side of things. If testing with this information doesn't resolve the issue, there's still more to check, but more information will be useful to see where the issue may lie.