In the first instance where you "disagree" I believe you actually agree. Yes the power (current) is supplied from the Cyl Stat to the boiler, but it is also true that in the process the orange wire becomes live (240 volts) as in the article.
But what the author wrote, without my comments, is:
When we are calling for hot water, then the controls energise the orange wire and de energise the grey, thus firing up the boiler and pump
This implies that the boiler is fired because two things happen: the orange is energised and the grey de-energised. The events are true, but they are
not the cause of the boiler igniting.
Exactly the same in your second disagreement. The orange wire is made live even if it is not the source of power for the boiler.
The only time the orange wire serves any useful purpose is when the valve is in the CH only position. It then is the
only source of power to the boiler. Ideally the orange wire should be disconnected from the boiler, except when it is needed. I suppose a relay or something similar could have been used, but this would have added to the cost and complexity. The solution was to put a high resistance R2 between the lower contact of SW2 and the motor. The motor then does not get sufficient voltage to run from either the orange wire or from the white, when SW2 has switched over.
I'm not sure that your statement that "These resistors are there to prevent the motor turning when the orange wire gets 240v from the HW stat. " Is entirely true since the same would apply if R2 were omitted entirely.
Surely that would depend on the relative values of R1 and R2?
However I assume from your statement that the covert path from the orange wire via R2 and D1 to the white wire, and hence to my additional motor "is not important" means that it is safe to do so, so I'll give it a try.
You have raised an interesting point. The motor stalls in mid position because it is provide by half-wave rectified voltage via D1 and R1. The orange wire supplies voltage to the D1 via R2, but in the opposite direction, so the output, on the SW2 side of D1 will be much less. If this was not done there, the voltage on the white wire would be dirty, feeding back to the CH thermostat etc.