Here is what I think your issue is. The mortgage broker you're working with ran your file through an AUS or automated underwriting system (just like every other lender will) and it either came back with refer/eligible findings which means it will have to be manually underwritten or it came back requiring a 12 month verification of rent or VOR.
A manual underwrite will always require the lender to document a 12 month rental history as a condition of approving the loan but if you can get your score up, you have a chance of getting approved through the AUS and it may not require the rental history verification as part of the approval.
You've already stated you can not satisfy the VOR requirement so your mortgage broker is looking for a way to get a round it & the only way that's going to happen is if you get your scores up and get approved through an AUS without out the VOR requirement.
Take a look at the recommendations from some of my past clients on my Trulia profile by clicking my name.
Please feel free to contact me for more information or help. You can also find more information on my FHA website by licking the link below.
Senior Mortgage Banker
Great Plains National Bank