Actually a complete solution was even easier. First I noticed that a 
Java app I use (muCommander) also retreats from displaying tooltips when 
the app is inactive. Then a Google search gave me this JDK bug report 
[1]. And once the SWP_NOOWNERZORDER flag was mentioned, the rest was a 
walk in a park.

Double checking what flags others use for their tooltips revealed 
nothing more, see this for example [3].

Attaching a patch that applies this flag to our tooltip SetWindowPos [2] 
invocations, in w32fns.c. Works for me. Tested on trunk and emacs24.

If you agree, I might commit this to emacs24.

Jarek

[1] http://bugs.java.com/view_bug.do?bug_id=6770457
[2] 
http://msdn.microsoft.com/en-us/library/windows/desktop/ms633545%28v=vs.85%29.aspx
[3] http://www.vtdev.com/net/tooltip.html