The fix-up algorithm only creates an anonymous inline-table when the parent box is an inline box.
However, this should also happen whenever the parent inlinifies its contents. It's worth noting that, according to CSS Display, inlinification happens before anonymous fix-up, so the fix-up algorithm can't rely on inlinification to make table become inline-table.
Currently I think inlinification only happens in ruby containers, and run-in boxes with a flow inner display type. Gecko is the only proper implementation of ruby, and effectively it seems to generate an anonymous inline-table inside a ruby container. I don't know any implementation of run-ins, but a run-in with a flow inner display type seems to be considered an inline box (this should be clarified in #1491); so this case may already be covered by the current spec.