If I may, I'd like to work through my thought process to better explain:
Difficult Terrain: Difficult terrain, such as heavy undergrowth, broken ground, or steep stairs, hampers movement. Each square of difficult terrain counts as 2 squares of movement. Each diagonal move into a difficult terrain square counts as 3 squares. You can't run or charge across difficult terrain.
If you occupy squares with different kinds of terrain, you can move only as fast as the most difficult terrain you occupy will allow.
Flying and incorporeal creatures are not hampered by difficult terrain.
Obstacles: Like difficult terrain, obstacles can hamper movement. If an obstacle hampers movement but doesn't completely block it, each obstructed square or obstacle between squares counts as 2 squares of movement. You must pay this cost to cross the obstacle, in addition to the cost to move into the square on the other side. If you don't have sufficient movement to cross the obstacle and move into the square on the other side, you can't cross it. Some obstacles may also require a skill check to cross.
On the other hand, some obstacles block movement entirely. A character can't move through a blocking obstacle.
Flying and incorporeal creatures are able to avoid most obstacles.
There is nothing to indicate that terrain that within a threatened area is considered difficult terrain or an obstacle merely because it is within a threatened area. Open terrain that is threatened is still open terrain.
To this, include:
Opponent: You can't move through a square occupied by an opponent unless the opponent is helpless. You can move through a square occupied by a helpless opponent without penalty. Some creatures, particularly very large ones, may present an obstacle even when helpless. In such cases, each square you move through counts as 2 squares.
Emphasis is my own. If you move through squares occupied by an opponent, each square counts as 2 squares. While you couldn't normally move through such a square unless the opponent was helpless, the Acrobatics skill does allow you to do so, assuming that you pass the requisite check. Though, each square still counts as 2 squares—this fact isn't changed with the use of the Acrobatics skill.
In addition, you can move through a threatened square without provoking an attack of opportunity from an enemy by using Acrobatics. When moving in this way, you move at half speed. You can move at full speed by increasing the DC of the check by 10.
It is apparent that the crux of the disagreement is the phrase "[w]hen moving this way...". You guys feel that this phrase means that the "movement penalty" only applies to those squares that are threatened. I completely understand why you believe that. I read it as applying to the entire movement rate. The way I see it, it doesn't say "when you use Acrobatics to avoid an AoO, you move at half speed through the threatened squares", or "when you use acrobatics to avoid an AoO, each threatened square counts as two squares". I read it as "when you use acrobatics to avoid an AoO, your movement rate is halved".