Well, OK, it was one of the NASA apologists, Amy Teitel*, of several, who put forth the 'they went via the poles' explanation.
To explain away the very real and serious dangers of GCR, she seems to have referred to a comment by Dr. James Van Allen himself, who wrote in 1958 that 'any human exposed to even 10 roentgens
per diem would only have an even chance of survival'. He then suggests future manned spacecrafts take off via 'the radiation-free zone over the poles'. Which of course Apollo did not do but which the 'debunkers' like to er,
suggest they did
Van Allen stated that the 'maximum radiation level as of 1958' in entering the radiation belts is equivalent to between 10 and 100 roentgens
per hour. Your exact same diagram, as used by the 'debunkers', shows a thick black line, implying this is the route the Apollo 11 travelled but there is zero confirmation it travelled this 'safe route' at all. The aim of your hypothetical diagram is to 'show' Apollo missed the most dangerous inner belt (as is thought) but this is completely fabricated PR. NASA itself has never confirmed it. In fact, if anything, its records shows the spacecraft travelled right through the inner belt.
But not to worry, it went through '
very rapidly' so no worries, there, is the back up argument.