Hi Jack,
Not sure if this thread is still open, but I need to do an ‘answer-and-reply’ in order to ‘unmoderate’ myself.
It’s possible that you have a stroke around the text box, but it is such a thin line that its hard to see in InDesign sometimes.
Go into the InDesign working file, click on the text box. Next, go to Window / Stroke. Ensure that the Stroke box says 0px. Try exporting again.
good luck
Thea