Just as a brief (edit: failed) update to this situation:
It seems you were right about this, so thanks for the suggestion. Or, at least, the Legal Aid Foundation lawyer we spoke to today also thought this was a reasonable argument after seeing the contract and hearing about the dispute. 90% of the discussion was in Chinese so I wasn’t really following, but the lawyer’s assessment was that the original agreement about taking over the phone contract likely wouldn’t be enforceable if it goes to court.
She finished working there yesterday, and for the previous few days the company had been repeatedly pressuring her to sign another contract saying she agrees to pay the Chunghwa cancellation fee. She refused to do this (multiple times), despite the company lawyer and HR harassing her over it and recording a phone call with her as proof she’d been informed of the cancellation fee she needs to pay and that she would be sued to recover the fee if she doesn’t pay it voluntarily.
She also refused to take the still-unopened phone with her and left it in the office, which ultimately led to the company lawyer and two HR employees chasing her down ten flights of stairs and out of the building trying to insist she takes the phone because it’s hers now, with the lawyer recording a video the whole time. She had to lose them by crossing the road on a red light then going into the MRT. This is all over a cancellation fee of ca. NT$6,750 and a phone worth about NT$6,000 new, so this behavior by a company is a bit bizarre!
I’m assuming that the company will next try to deduct this from her final paycheck (which I understand isn’t okay either). In any case, we’ve calculated her unpaid overtime for the two months she worked there as being on the order of NT$28k*, including multiple cases where her daily and weekly working hours exceeded the legal maxima (up to 13.5 hours in a day and up to 63 hours in a week, respectively, excluding lunch breaks).
I understand that the fines for these LSA violations are considerably more than the disputed amount, so the next step will be filing a complaint with the labor bureau, with a view toward going through mediation for the unpaid overtime and getting them to drop the phone issue. 
*Edit: After reading this post, it seems I calculated this wrong because I was using logical math (ca. 22 working days per month) rather than shitty Taiwanese employer math (30 working days per month) - should be around NT$21k.