I'm not from Laminar Research, just a fellow simmer in the UK.
As you may have seen from other posts on this Q&A forum, there have been a great many simmers who have reported this same problem with 'permissions', either when installing a digital download version, or even when trying to install a DVD set.
1. In a vast number of cases, the problem has been related to anti virus software or a firewall which can block access to the relevant files etc. You might wish to temporarily turn these off to see if the updating process works then?
2. The other culprit could be a PC system specification that doesn't meet LR's minimum requirements, so please check here https://www.x-plane.com/kb/x-plane-11-system-requirements/ to make sure that your PC does?
3. LR recommends that XP11 is installed on your PC's desktop as opposed to a local hard drive, as this may overcome any 'permission' issues.
4. When you refer to the term 'crash', do you mean that XP11 closes down and you go back to the desktop (CTD), or that your whole PC shuts down (BSOD) to the point of reboot?
5. Could you please upload a copy of your XP11 Installer Log.txt file to this post, so that I and others with a broaded knowledge base can review it in an attempt to establish what is causing your reported problem.
If you're not sure how to upload files to this Q&A forum and this post in particular, please click on the following link and view the PowerPoint slides that I have prepared for this specific purpose: http://questions.x-plane.com/?qa=blob&qa_blobid=5397046176897073041
Sorry, can't think of anything else currently, but hope this helps for now?