I agree, it's confusing. Let me try a picture to see if we can get on the same page, or have a gizzled friend of Rudolf Diesel chime in.. and while it probably sounds pedantic or lecture like I am only trying to be complete and assume as little as possible in the explanation so that everyone can understand what I'm saying and also pick it apart if I err. Please be patient!
First, it's a four-stroke. Meaning, the crank goes through two complete revolutions for each cycle:
1. Intake: First 180 degrees of crank motion. The piston goes down and sucks in clean air while the intake valves are open, exhaust valves are closed; ignoring overlap. Intake stroke ends at 180 degrees or BTC.
2. Compression: The second 180 degrees of crank travel, where piston goes up and compresses the air - heating it. Ends at TDC, 360 degrees (1/2 way) into the four-stroke cycle.
3. Power: With the piston again at top-dead-center fuel is injected. It is ignited by the hot air, which expands and pushes down the next 180 degrees to BDC and completing the first 1 1/2 turns of the crank (360 + 180, or 540 degrees).
4. Exhaust: The piston is on the up stroke of the last 180 degrees, pushing exhaust out as it approaches the end of the fourth cycle and completing 720 degrees of travel.
So, a 'stroke' is 1/2 turn of the crank where the piston either travels top-to-bottom, or bottom-to-top.
Meanwhile, the CAMs are turning at 1/2 the speed of the crankshaft because their pulleys have twice the teeth of the crank... so for every 180 degrees (1/2 turn) of crank spin there are only 90 degrees (1/4 turn) of CAM spin. In the full 4-cycle, or two revolutions of the crank, the CAM only completes one complete revolution. I think this is the key to understanding why you cannot be out of phase if all the pins are installed. Moving on..
Last tidbits that help understand the mechanical side. If you look at the crank it's like most 4-cylinder engines, where cylinders one and four are UP when cylinders two and three are DOWN. This balances the mass as it rotates.
Also - typical firing order for such a 4-cylinder is 1-3-4-2.
That said, the following table then shows you where all the moving parts are as the engine (crank) goes through the two complete revolutions (720 degrees) of the 4-stroke cycle (click to view on webshots, and then click again to go full screen):

You can see, with the yellow highlight, that there is ONE and ONLY ONE place in every TWO crank (not cam, CRANK) revolutions that BOTH the crank PIN in the flex plate and the CAM PINs all line up at the same time.
In the 180-degree out of phase scenario that I think you are concerned about, the crank pin would go in BUT THE CAM PINS would NOT. Said a different way, the crank pin would line up twice during it's two revolutions but the cam pins would only line up once because it only rotates once during the two complete turns of the crankshaft. During the second crank pin alignment, the cam pin holes would be 180 degrees away from their alignment pin position.
So - everyone - help me here and see if I've missed something?
Thanks - Mark