I meant that you're confusing "thread priority" with "process priority". In general, they're completely independent of each other. Changing thread priority will *not* affect process priority.
This link might help:
This is true of Linux and Pthreads (and, for that matter, equally true of Windows and Win32 or .Net threads). Your mileage on other OS's (particularly real-time and embedded OS's) will vary.
Here's an example of an OS with decidedly "non-standard" behavior:
The key thing is:
1. Understand the basic concept of "threads" vs "processes" (in general)
2. Understand the difference between kernel-level and user-level
3. Apply that understanding to your particular combination of OS platform and threading library