In recent years, fraud has become a major concern because of escalating instances where buyers purchase the homes of struggling family members at a discounted short sale price, then allow the family members to stay there and transfer the title back to them. Thus, the sellers reacquire the original home at maybe half the price. Lenders reason that if they had wanted sellers to benefit thusly, they'd have agreed to a comparable loan modification in the first place. Other folks might argue that this is a better workout scenario than a foreclosure, but lenders and regulators consider it fraud.
So that's why banks make both the buying and selling parties sign a sworn arm's-length affidavit (called an Identity of Interest Certification form in the case of a Federal Housing Administration mortgage), attesting the parties are unrelated by family, marriage or business.
Even though there are various interpretations of "family members," it would still be best to come clean to the lender in this case because both parties, while not blood relatives, do have a family association. As you mentioned, it's always best to avoid even the appearance of impropriety when you're signing contracts and sworn affidavits.
Lenders do make exceptions in some related-party cases, but the numbers in the deal must add up and there must typically be ironclad agreements that the sellers are not allowed to stay in the home or repurchase the property. In your brother-in-law's case, the home had languished on the market so long that the lender might consent to such a deal, as long as the offer is acceptable. However, if the sale price is less than 35 percent to 40 percent of what your brother-in-law paid when it was first financed (a figure commensurate with downward market adjustments since about 2008), the sale probably won't fly.
If the deal is approved, your parents might face a larger down payment and other stricter loan-to-value requirements from their lenders, depending on the type of program they pursue. Ironically, if the home were to go to auction, your parents could swoop in and win that bid, then live happily ever after there or deed it to whomever they wanted. (But they'd have to pay cash at auction.)
When is the last time the home was appraised? An independent appraisal would provide the latest valuation and serve as an accurate fair market value barometer. Of course, the lender may want to trot out its own appraiser who could produce a slightly different determination.
All said, your parents needn't avoid this deal because it may actually come off, given the circumstances. But as you sense, it would be best to be upfront about the family relationship in all dealings, even if the buyer and seller have different last names. Good luck!