The answer to the question is Yes. I have certainly seen projects purportedly done by children that were almost certainly done by parents. Not a good way for the kids to learn.
However, I have always thought these questions were more complicated than they seem. My goal as a parent has been to help my kids prepare to be successful, productive, happy adults. It was not to get them into the most prestigious schools but to help them find paths that helped them prepare for happy, successful, productive adult lives.
Schools themselves have several functions but I will highlight two: education and sorting (e.g., grades, honors v. non-honors classes, college admissions, grad school admissions). Many schools and parents (especially parents on CC) focus too heavily on the sorting aspect and imbue the sorting process with some kind of moral or scientific power. I view the sorting just as means, not ends. Moreover, the sorting process is far from imperfect.
The parent described in #83 recognized that they could help the kid get to the place where he was a successful, productive and hopefully happy adult life if they didn’t ask him to do the thing he could not do well, which was write essays. Once past the artificial sorting hurdle, they thought, he would be successful. The only problem: the kid or adult probably signed something saying the work was done by the kid.
I had a very different situation – a truly gifted kid who was/is severely dyslexic. Reading and writing physically hurt him. The sorting process the schools have was often dysfunctional. They would keep him out of enrichment math early on because he was slow at math problems but made change for Monopoly in his head before kindergarten could multiply exponentials in grade 2. So, we needed to get the schools to alter the processes in some ways. I’ll spart yo details, but he got into an elite LAC with minimal distribution requirements, performed at the highest levels (the first summa his advisor had given in 18 years), started his first company while in school, attended the best grad school/MBA program in the world for what he did, started his second company while in grad school and has been nationally recognized. He’s not about making money (could have gone the hedge fund route if he were) and I’m not implying it is the metric for success but his net worth on paper at age 28 probably exceeds the vast bulk of CC parents. We just needed to help him navigate around and through dumb sorting processes.
@Nhatrang, it seems unlikely that the difference between 1530 and 1590 made any difference, but they may also have pushed her to do other stuff that helped. However, the main point isn’t to have kids succeed because of your help, but to give them the skills and help them get into a position to succeed given their talents and skills.