Before I get around to answering your question, I'm wondering why you decided to agree to use the same agent as the seller ... you mention "that was how they wanted it" but don't say whether the "they" is the seller or the seller's broker. In either case, you have the right to use your own broker to advise you. If the listing broker told you otherwise, that broker misinformed you.
When the seller's broker and the buyer's broker are the same person (or company) there is an inherent conflict of interest that puts the buyer at a disadvantage. This is because the seller typically gets a lot of advice about the proper asking and selling prices when meeting with the listing broker before the property is on the market. The buyer, on the other hand, only receives advice upon deciding to make an offer on a particular property.
Illinois law calls the situation you are in "Dual Agency," though this is a misnomer, since it implies that a single broker is representing both the buyer and the seller. In fact, the broker in such a transaction represents neither party.
What's important to you is that Illinois real estate law prohibits a broker in a dual agency situation from advising either party on what price to offer or accept. That means the listing broker, acting as a dual agent, cannot legally give you any advice on the value of the property or what to offer the seller (though that broker likely has already given that advice to the seller). A dual-agency broker can only process paperwork and pass messages between the parties.
So hopefully now you see why I asked why you decided to agree to this, since it puts you at a great disadvantage. You really ought to get your own broker working for you ... it doesn't cost you a thing, since your broker will be paid in a cooperative commission from the seller's broker.
Getting back to your question: you asked whether the seller of a bank-owned property can refuse an offer based on an FHA loan. The short answer is yes, any seller can legally refuse to sell a property based upon what the seller considers unfavorable financing or purchase terms.
FHA loans were designed to accommodate buyers who otherwise would not qualify for a mortgage due to their income or financial history. They are the least desirable type of financing, save perhaps VA loans or other types of "100%" financing. Given a choice, sellers will almost always accept an offer using conventional financing or cash before they will accept an FHA offer.
Banks in possession of foreclosed properties typically want the best financial terms possible for the sale, so that they can plan to have the liability off their books as quickly as possible. That's why they vastly prefer cash offers on foreclosure properties. They don't want to deal with the uncertainty of mortgage approvals (ironic, huh?).
You mentioned that the "home was just appraised within FHA borrowing guidelines ($528k) for multi-unit." You also mentioned earlier that the building was a two-flat. I checked the FHA loan limits online and found that the current limit for two-flats in Cook County, IL is $524,850, or $3,150 less than what you say the appraisal was.
This less than 1% difference may not seem significant to you, but it could at least delay your loan commitment, if it didn't prohibit it altogether. Also, FHA loans require an inspection to certify minimum habitability standards (think grounded outlets, solid roof, etc.) which could require the seller to do repairs before closing. Banks typically don't do repairs to foreclosed properties. Those two things my opinion, could be what are keeping the seller from accepting your offer based on an FHA loan.
One last thought: where is this $528,000 two-flat located? Will the income from the second unit be sufficient to make it worthwhile at that price? A good REALTOR can help you to analyze financing options and potential returns. Get one to represent you before signing any papers!