I think apportioning blame is a natural human trait. It starts at quite a young age; 'It wasn't me it was him/her/the dog/the cat'. It was frowned upon when I was young, it was 'telling tales'. On the other hand it was a good to own up and take responsibility. A harsh lesson really. If it wasn't you you weren't supposed to reveal the culprit. If it was you, no blaming someone else - own up! So either way you were the one in trouble. All you had for comfort was your integrity.
In the McCann case the parents freely admitted that they left the children in an unlocked apartment, but also strove to downplay it. They were naive, they checked the children regularly, they weren't far away (just like being in the garden), it was 'within the bounds of responsible parenting', and, most interestingly, ''I know that what happened is not due to the fact of us leaving the children asleep. I know it happened under other circumstances."
Immediately after the disappearance the Portuguese authorities began to be blamed by the parents and others for various perceived shortcomings. They left the group all alone, they didn't close roads and airports, they didn't seal the apartment, they didn't collect forensics, they smoked (?) in the Police Station, they didn't offer refreshments, they drove too fast. They were ridiculed and given childish nicknames.
When the dogs were brought in from the UK they were labelled 'incredibly unreliable' and 'unscientific', with a case in the US being used as an example. Unfortunately the case was solved and the dogs were exonerated.
The SIO then wrote his book. He was blamed for hampering the search, libeling the children, and hurting the parents. Following a civil defamation trial most of the points weren't proved, except the one of harming the parents.
It seems the McCann parents did quite a lot of blaming, and those who support them do the same. Anyone who dares to point out that leaving children home alone isn't 'responsible', that the PJ carried out a huge task to the best of their ability, that police dogs are incredibly useful or that Amaral's book didn't hamper the search is attacked. They are accused of lacking empathy, telling lies, being stupid, and trolling.
It seems to me that the parents have blamed everyone for everything which has befallen them, and done their utmost to escape any blame themselves. Perhaps it has helped them to cope, but they ran the risk of 'protesting too much' and it has resulted in people becoming interested, researching the case, and deciding that the parents aren't convincing.