The firm said it had now lifted the ban, maintaining it was due to 17-year-old Feroza Aziz's prior conduct on the app - and unrelated to Chinese politics.
Additionally, the firm said "human moderation error" was to blame for the video being taken down on Thursday for almost an hour.
Ms Aziz posted on Twitter that she did not accept the firm's explanation.
"Do I believe they took it away because of a unrelated satirical video that was deleted on a previous deleted account of mine? Right after I finished posting a three-part video about the Uighurs? No.”
Eric Han, TikTok's head of safety for the US, said Ms Aziz had been banned earlier this month after she posted a video containing an image of Osama Bin Laden.
"While we recognise that this video may have been intended as satire," Mr Han said, "our policies on this front are currently strict.”
Mr Han wrote: "Because the user's banned account (@getmefamousplzsir) was associated with the same device as her second account (@getmefamouspartthree), this had the effect of locking her out of being able to access her second, active account from that device.
"However, the account itself remained active and accessible, with its videos continuing to receive views.”
But on Thursday morning, the viral video - which has been viewed more than nine million times, across multiple networks - was also removed from TikTok.