Your are right in one sense that Zillow has mislead the public, but they have done it in the same way nearly every public company does, sometimes by choice, sometimes by convention. 

But, if it is a conventional institutional loan, you could double app, or your Mortgage broker could, and then each lender would order their own appraisal (hopefully, from a different appraiser).

Buying a duplex and living in one unit, renting the other is an option (you can get conventional owner occupant financing this way), finding a deal with value add opportunities and doing a cash out refi down the road is also an option.

This is a conventional  program that will lend up to 95% of the post renovation value.  

I have an opportunity from a wholesaler that I’d like to purchase in the next two weeks, although I don’t think I’ll have time to get a conventional loan.

If so, depending on how much equity you have maybe you can refinance it to a conventional loan. 

I'm doing a house hack with a conventional rehab loan.

Conventional products go from 5-20% down depending on what their use is.

I currently am using a VA loan for my property I live at, but I am looking to possibly refinance into a conventional loan, then use a VA construction loan to build the home next door and move into it.Thank you!

Foreign National loan, not conventional is available.