I'm not precisely understand what you mean by interrupt. If you mean it in a general English word sense, I think I agree with you.
If they have moved out of range to trigger an OA (which happens right before they move out of range), they have done that. The OA still triggers. If, after that, since they technically have not yet moved out of range they wish to not continue moving so they stay in the same square, that's fine. They have moved "just shy" of 5 feet, so I would count that part of movement used in case they decide to move later int he round, or do something late requires movement like if they were proned in the OA.
A different example is a creature that declares it's moving across an area that's they don't know has been hit with Spike Growth - they can stop moving, reverse their movement, or do anything - they aren't bound by the declaration of their original destination, each square is it's own choice.