Tom, I am always optimistic but I think Joseph may have been economical with some of his life details, hard to know which though!
Have you searched through the indexes for births and marriages here
https://familysearch.org/#start The LDS indexes, which are free to search, are really strong and comprehensive for Scotland. They, combined with a census search, normally throw up lots of options. However, cannot really see much to help so far with the info that Joseph gave

The ultimate check is the official pay to view site
www.scotlandspeople.gov.uk It is free to do some general searches after you register (you have to pay in units/money to view search results or images).
From just general searches on SP, there are no births showing in Inverness-shire between 1865-9 for a Joseph/Thomas Russell, a fact confirmed by the indexes on the LDS site.
So....
- parents not married (no marriage showing for a couple with those names as given by him for his parents, including searching for Jessie as Janet which is a common variant).
- tried searching for his birth as an illegitimate birth, ie., with him as Cameron and mother as Jessie/Janet Cameron, and nothing showing for him.
I saw this entry for migration:
The 'Dacca' arrived from London in Brisbane on 26 Jul 1887. On the manifest showed a Joseph Russell aged 22 (so born c. 1865), b. Inverness.
That is as far as I have got so far...which is not much really

Monica