<<The OP had told her friend that she would let her know if she would be attending.>>
To me, this means: Unless I call to tell you otherwise, I will not be able to go.
The friend should have assumed that the OP would not be joining her, based on their face-to-face conversation. The OP was not "rude" for neglecting to call and confirm what she'd already said...unless something had changed and she would have been able to attend after all.
The person who bought the additional ticket, bears the responsibility for doing so, when she'd already been told that the OP most likely wouldn't be able to accompany her. Whether that was for financial reasons or other reasons.
The ticket purchaser's behavior was a passive-aggressive way of attempting to get what she wanted...regardless of the OP's indications otherwise. As well meaning as that may have been, it was rude of the ticket purchaser to go ahead with the purchase on the OP's behalf, without express permission to do so.
ETA: Had the ticket purchaser said to the OP beforehand: "It may be a sold-out performance, so I want to make sure you have a ticket. I'll be going to the box-office by x o'clock tomorrow to get seats for all of us, and you can pay me back whenever. Please let me know before I leave for the box-office, if you won't be able to join us. Otherwise, you're all set with a ticket."
The OP could have said "yes" or "no" to the arrangement right there...or agreed to call with a firm answer, by the time the ticket purchaser left to go get the tickets for all of them. Only then would the OP be considered "rude" for not calling...and also be responsible for paying the cost of the ticket purchased on her behalf, for neglecting to do so.
And even if the OP suddenly became ill and couldn't attend, she'd still be responsible for paying for her ticket.