I just had a look at my 07, which is closer to the 06 than an 05 would be (06+ has the variable valve lift mechanism in the valve lifter system). On the driver's side, there is indeed hardly any room to move the cover away from the head, especially because the valve lifter mechanism inside extends out beyond the head itself. The cover isn't flat -- it peaks out just where the chassis rail is, and at the back the distance from the peak to the rail is less than the distance from the peak to the inside edge of the cover. If the valve train didn't go above the head, the cover could be lifted out; but because the cover has to clear the valve train, it has to come out further before it can be maneuvered out.
The OP in the linked thread never did complete the job, at least not in that thread -- it was left to some future time when the timing belt was to be done. It was never followed-up.
Most comments about how easy it to remove the valve covers have been related to earlier model years. Thing's have certainly changed.
I'm not sure just how it would come out. Here's a clip from the 07 manual, which seems to suggest that the injectors (or perhaps the fuel rail) have to come out, but there's no more detail about this requirement. (It from the Valve Clearance page of the Mechanical Section of the Engine volume.)
8. Valve Clearance
A: INSPECTION
NOTE:
Inspection and adjustment of valve clearance
should be performed while engine is cold.
1) Set the vehicle on a lift.
2) Lift up the vehicle.
3) Remove the under cover.
4) Lower the vehicle.
5) Disconnect the ground cable from the battery.
6) Remove the timing belt cover (LH).
7) Remove the fuel injector. <Ref. to FU(H4SO)-
28, REMOVAL, Fuel Injector.>
8) When inspecting #1 and #3 cylinders:
(1) Disconnect the spark plug cords from spark
plugs RH side. <Ref. to IG(H4SO)-4, RH SIDE,
REMOVAL, Spark Plug.>
(2) Disconnect the PCV hose from the rocker
cover (RH).
(3) Remove the bolts, then remove the rocker
cover (RH).
9) When inspecting #2 and #4 cylinders:
(1) Disconnect the spark plug cords from spark
plugs (LH side). <Ref. to IG(H4SO)-4, LH SIDE,
REMOVAL, Spark Plug.>
(2) Disconnect the PCV hose from the rocker
cover (LH).
(3) Remove the bolts, then remove the rocker cover
In addition, on mine, the oil filler tube goes into the left side valve cover -- it would have to be freed to enable to cover to come out.
What this needs is someone who has done the valve cover replacement on an 06+ engine.