Other lenders say they need an appraisal and then choose different forms like a 1007 or a 216 to accompany the Fannie Mae 1004. 

Any transfer of ownership triggers the 6 month seasoning unless it's as described in the second paragraph above.Here's the Fannie Mae eligibility matrix that's used by all lenders who sell to Fannie Mae as a basis for underwriting decisions before they add their own overlays.https://www.fanniemae.com/content/guide/selling/b2/1.2/03.html

@Ben Morand That deal was sourced through a broker and financed with Fannie Mae debt. 

Here's the wording from the website:HomePath Mortgage allows a buyer to purchase a Fannie Mae-owned property with a 5% down payment (as of November 16, 2013), no lender-requested appraisal and no mortgage insurance.

You cannot get a rate and term refinance when paying off a loan that was not used to purchase the property if you're planning on going with a fannie mae loan.

I've gotten most my properties from HomePath.com, fannie mae foreclosures. 

You could always refinance the 4 unit to a Fannie Mae or Freddie Mac loan, thereby freeing up you ability to get another FHA loan in the same area as the existing 4 unit.

Fannie Mae and Freddie Mac are still buying loans with borrowers who are self employed. 

The seller is Fannie Mae and the seller's is not allowing to dig to find out whether its an oil tank or not.

Conventional loans are the loans governed by Fannie Mae and Freddie Mac (if you recognize those names).