What is probably happening:
You're SHQ (or rather the city the SHQ is sitting in) is also receiving LPs from another truck station sitting somewhere outside. The LP (prior to beta 10 or so) from that other truck station go THROUGH the hex the SHQ is sitting in and go out the other side. This means, that there are more LP available directly outside the city than in the city itself.
Take a look at this screenshot:

The city is generating roughly 4000 LP, splitting them evenly - 2000 north, 2000 east.
In addition, from another truck station there are roughly 1000 LP each coming from the north and the east - passing through the city and continuing on.
So, in the city hex I have: 4000+1000+100 = 6000 available.
The hex to the north has: 2000 + 1000 (from the north) +1000 (from the east, through the city) = 4000 available.
The hex to the east has the same: 2000 + 1000 (from the east) + 1000 (from the north, through the city) = 4000 available.
What this means is that if the city uses all 6000 LP, there will still be 2000 LP left over. So the hexes right outside the city can't ever be black.
If the hex your SHQ is sitting in is black, then it used up all available LP.