That seems somewhat nonsensical. Not your solution so much as the error itself.
As I am logged into this server as the Domain Administrator- the Holiest of Holies- there is no place I do not have write access to.
What's more nonsensical is that I noticed the path it's attempting to write the log to:
"C:\Program Files (x86)\Openfire\bin\..\logs\"
Is not a place where logs are stored upon installing the program. The logs are in fact stored here:
"C:\Program Files (x86)\Openfire\logs"
Which might explain why it can't write to anything- there's nothing there to write to.
In any case I wiped out the install because the level of silliness here- specifically the sort of level that occurs when the code of a configuration doesn't respect the program's OWN default install locations for logfiles- is about where I pull my ripcord.