I don’t know where you got your information, justlurking, but all offers of professional help have not been spurned, publicly or otherwise.
Security is a legitimate reason for John to deny anyone access to the FR servers, databases, software, etc. Suppose John accepted an offer and then that person was banned at some later date. John then has to deal with someone who knows the code and the configuration AND has a grudge. Been there, done that. It ain’t fun.
Even if security weren’t a concern, lack of knowledge about the software & hardware environment is. Having someone attempt to troubleshoot the problem could ultimately make John’s job more difficult because he has to answer basic questions about the environment every few minutes. “Where’s this/that? Why did you do it this/that way? What might happen if we change this/that?” It’s a frustration he doesn’t need.
Jim & John aren’t being difficult, prideful, or stubborn. They’re doing what they can with the resources they have in a tough situation.