I'd like to avoid having her parents provide their own bank statements (to prove origin of the funds in question) or take any tax hit because of their generosity.If I have any misunderstandings about the process, please let me know. 

This is a major misunderstand many landlords have that is simply not true.

I'm thinking there may be a misunderstanding in there somewhere.

Maybe I'm misunderstanding her because that doesn't even make sense.

I may be misunderstanding you but you are saying you are happy to pay full retail of let's say 100K on a property and put 20K in because then you have equity?

Or am I misunderstanding?

Does this question make sense or am I misunderstanding something?

That way, there is no misunderstanding over what you **think** you said and what they heard.

A 4 plex is usually considered a single property not 4 individual ones, that was the reason for my misunderstanding   

If this is a misunderstanding, you should still have them give you their criteria for tenant qualifications.