Yes, you're right. I tried Firefox 12 and also got HTTP 403 when using the following user agent: `Mozilla/5.0 (X11; Linux x86_64; rv:12.0) Gecko/20100101 Firefox/12.0`.
It looks like those old user agents get used quite a bit by some abusive OSM Tile scrapers, and are therefore banned.
If updating to a more recent Firefox version (think security!!) is not an option for you, an a Firefox extension like User Agent Switcher might be a workaround for the time being. In any case I strongly recommend to update.
[(actual config file)](https://github.com/openstreetmap/chef/blob/f6ba704c4a2c12c7eb71eda60ab88cfef12ac73b/cookbooks/tilecache/templates/default/squid.conf.erb)