In answer to the OP...
I think Ashya's parents were right to push the medical team on the options possible. I have personal experience of the exact same team at Southampton General and, whilst they are excellent clinicians, it is never wrong to push them on what else could be done and the pros and cons of pursuing a particular option.
Were they right to go as far as they did? Not in the way they did it. Whilst they took many steps to try and care for Ashya they failed to keep the medical team onside which presented by far the biggest risk to his health.
Could I have done what they did? Perhaps. I am a parent. I have watched family members and others face terminal cancer and know exactly the emotions that run through you when wanting to do everything possible to take the pain and suffering away.
I have a family member who is in the same congregation as the Kings in Portsmouth and was closely involved in helping them in when Ashya was ill in hospital. From conversations with them, I don't believe that the Kings were acting completely rationally when they did what they did. I understand why they did it but it could have been handled in a much better way. The Kings are known, apparently, for being the sort of people who form an opinion, stick to it and don't really care what others think about it. If they believe they are right then they have the courage of their convictions to face criticism.
This can be an admirable quality. The problem is that your decisions have to be sound.
The fact was that the hospital had already done the biggest thing in saving Ashya's life - taken the tumour out. Medically, if the tumour had not been operable then the poor lad's prognosis would have been very bad. Surgery is the primary treatment. The standard protocol for supporting treatment for many cancers is radiotherapy and chemotherapy. The former is designed to try and destroy the cancer cells that remain after surgery. The latter is designed to help damage cancer cells and stop them replicating. Typically one would have a course of RT lasting a few weeks, maybe alongside chemo, then a following and longer time on chemo.
The desired outcome is that the tumour is prevented from returning. For some cancers it may be possible that this could be many years (e.g. 5-10+), for others it may be just a few months. This is complicated by many factors such as age, type of cancer, how advanced it is, surgical success, response to adjunctive treatment and so on.
The Kings naturally tried to find out as much as they could about RT and CT. The internet is awash with information on cancer. It ranges from highly medical and technical right through to some outrageous claims that have zero scientific backing. The biggest problem is that people are looking for the magic word "cure". Many cancers cannot be cured. You may have long term remission but many will come back eventually. The trouble is that much of the claims on the internet use the word cure or relate stories that imply a cure when in fact there is zero evidence to suggest the individual outcome would have been any different.
Many standard forms of RT will have side effects including swelling and nausea . Often a person will have to wear a constrictive head mask during treatment. I would expect that Ashya would need to be sedated each time, probably daily, to prevent him getting too distressed. The radio beam has to go through tissue to hit the cancer area and then carries on going. It will damage healthy tissue. Sometimes that damage can be permanent but not always.
Chemo is often horrible. I completely understand why the Kings would want to avoid this but the treatment is individual and there is no saying exactly how a person will respond. Not only that, often the statistics for longer term positive outcomes are directly related to the use and success of the chemo.
Proton Beam is just another form of RT. The benefit is that the way the beam is delivered means it does not travel past the point of focus. The effect on surrounding tissue is reduced therefore the side effects are less. It is still an emerging technology so determining the best circumstances for it's use are still coming out.
I think the Kings were right to try and get second opinions on the likely effectiveness of proton beam. The team at Southampton are world class - but they don't work with PB every day. The opinion of the specialists that it was inappropriate should have been questioned however this could have been done in a far less confrontational way. I think they were wrong to allow the situation with the medical team to get to the point there was such a loss of trust.
Frankly the Kings got lucky on this one. Perhaps the team at Southampton were wrong but if not then the PB would have been useless. In the end there was some collaboration between the doctors but the Kings did not know that would happen when they removed Ashya. If the PB has been as successful as standard RT likey would then that's great but it could have been different.
The refusal to use chemo is questionable IMHO. It's their decision but the empirical evidence is clear. Statistically it increases the risk the cancer will return more quickly.
The Kings continue to insist that they did the right thing both publicly and privately. They insist Ashya is cured and are using his current good progress to justify their actions. Their focus on PB as some kind of miracle procedure, refusal to try chemo and lack of caution when describing Ashya's progress reflect the parents personalities. I sympathise with their actions but my understanding is that Brett King is the sort of guy who does not like to back down. Cancer is no respecter of defiance and time will tell how well Ashya does.