I would bet it's the base of the case like Cinch said. Not uncommon, my bet is your Tikka has a nice tight chamber, while whatever the used brass was from does not. I've run into this before. A small base die should fix your issue if you want to use that brass.
The first time was when I rebarreled my 270 Wby mag. Some of the well used brass from the factory barrel would not chamber in the nicely reamed custom. That was a tough pill since that brass is a little pricey.
Second time was a bhw 20 practical. Since I use once-fired 223 brass to form, I found some wouldn't chamber. A small base die cured it. New brass wouldn't have been an issue.
