Well, if I read your long post correctly, your objection seems to be that "not the right people" were praying.
That's a good, testable hypothesis, theoretically. Of course, it would be impossible to make family-members NOT pray for someone if they were pre-disposed to do so.
But it might be possible to find enough subjects with loving family members who do NOT believe in intercessory prayer (perhaps from some non-Abrahamic religions?)
Anyway, if it were possible to find a sufficient sample, it seems your hypothesis COULD be tested. Perhaps the results would be different.
In this case, however, I believe this study was in response to earlier studies, also using non-loved ones, to pray for people, and those studies tentatively showed a positive effect. This study was bigger and tried to fix some of the perceived flaws in the earlier studies.
In general, do you believe intercessory prayer can have a positive effect on the prayee? And if so, can you think of a way to test that effect so we can measure its efficacy?
Yes, I believe that the overwhelming percentage of the time, authentic earnest prayers of folks earnestly attempting to live a redeemed, righteous life in Christ's Blood and Spirit in a genuine, intimate walk with Him have a great impact on the focus of the prayers.
It would be tricky indeed to ferret out situations where all the variables could be suitably isolated. Theoretically possible but very tricky.
Personally, I believe that past studies have been significantly flawed, too. Not all Christians by label are authentic Christians. And, not all even authentic Christians are called to intercessory prayer or taught well in the details of it.
Nevertheless, I think child-like faith is often sufficient to touch and move the heart and hand of God. A 4 year old's simple prayer can often have more impact than several churches full of self-righteous folks vainly pleading in flesh-driven ways.
In any case, I don't care to think through all the details of sufficiently well designed studies to answer your question. But I do think it's possible.
I also think that--depending on one's attitude, it's quite comfortable to God for us to ask Him to demonstrate His majesty. On the other hand, it can be a cheeky affrontery to challenge or test Him out of a bad faith attitude or bad faith kind of perspective or place. I wouldn't encourage that on the part of anyone.