It's difficult - if not impossible - to answer your question accurately because there are many different facets to the mortgage modification process. I'm not sure what was on the Equifax credit report as there might be something on there that might make you ineligible for a modification (although I couldn't guess what that might be). It is possible that the applicatino was denied for another reason altogether. It is also entirely possible that the denial is in error. It's time to lawyer up. Be sure you retain one who understands loans modifications, and understands all of your options.
The effort to reasonably answer all of your questions can take up a bit of time. As a result, most experienced attorneys believe it best to charge a fee for the time it takes to resolve all of your and the attorney's concerns to mutual satisfaction and to the understanding of you both.
By doing so, reasonable legal advice is provided to serve your needs. An appointment, where an attorney can spend an hour, perhaps longer, to review your realistic options is in your best interests. This is just like you'd do if you went to see a medical doctor. Use the professional skills available to you.
I strongly recommend an appointment with a candid and experienced attorney.
NOTE: This observation is made available by the lawyer for educational purposes only. This observation is not like a communication with a lawyer with whom you have an attorney-client relationship along with all the privileges that relationship provides.