I personally try to work with the "in for a penny, in for a pound" approach -- that is to say, if I find myself messing with a profile at all, it's probably because it doesn't appear that the profile has had adequate research from reliable sources. So messing with it means finding better sources, adding additional material to the narrative with inline sources, with a particular emphasis on births, parents, marraiges, deaths and children. Once that's done, the data field really needs to be corrected so that the parents, spouses and children agree with what I've documented in the narrative.
I have revised profiles and also reviewed the work of others as part of the Magna Carta project. I try to be quite adamant in that role that work on a profile has not been finished until all the children are documented in the narrative and the links in the data field show only documented children. I've seen some well done profiles where no attention has been paid to the linked children, but it is in falsely linked children that most erroneous genealogies to famous people show up.
Where my idea runs into problems is (1) often I have time enough to figure out that the profile has errors, but not time enough to find out the truth, (2) I can't find any reliable data out there leaving the whole profile in question or (3) fixing the relationships to parents, spouses and children starts to involve some research into THEM as well. So in three minutes you could probably do a search and find evidence that I haven't met my own ideal!
To give the short answer to the question above, if I haven't done the research, I'm not comfortable making changes to the data base including parent/child connections. If I have done the research, and I've added it with source documentation in the narrative, then I'm quite comfortable making the changes with a public comment as to what the sourced data deemed necessary.
I've learned to check the Changes section before working on a profile. If there's been work on it within the last few months, I feel a much greater obligation to check with others while delving in than if no changes have been made for a while. But one of the things that attracted me to WikiTree is the doctrine that anybody can work on a profile since erroneous changes (except merges) can always be undone