It's hard to give objective advice without knowing more about the case, especially which journal, but this journal's behavior is surprising. Usually fake journals will publish anything as long as you pay for it.
Some have as strategy to generously offer free publishing to 'high quality papers' (which tells you something about the papers that don't fall in this category by their standards...) or to Western authors. In the later case, the goal is to give a false appearance of international recognition to cater for the needs of (mostly, but not limited to, India- and China-based) authors to publish in 'international' journals. Of course they have no real strategy to archive the work that they receive, they probably have no data management or backup strategy, nothing. I suspect some operate from internet cafés. It's frequent that entire journals just vanish without a trace, and without reimbursing the APCs, obviously.
In your case, why would they not publish your paper is mysterious, but is probably not unrelated to the fact that you didn't pay anything. It's possible that they actually evaluated it and found an issue with it (plagiarism, ethical concerns, blatant off-topic, etc.) or that it didn't serve their purpose of legitimating the trash that they accept for a fee, but only you can know if this is an option.
Or, they have bad intentions, from which I can think of a few:
- They will ask for money to publish it.
- They will want to sell you back the rights.
- They will sell the content to some unscrupulous scholar who will publish it as his/her own.
At any rate, brace yourself, anything is possible. I would recommend, in the short-term, to upload a pre-print on your personal website to give access to it to your scholarship committee, even if the copyright contract prevents you to do so. Fake journals rarely have the firepower (or enough legal notions) for seriously fighting over copyright issues. You should also tell your story to Beall, at least for the sake of warning other scholars.