If the DMV, Costco and the government accept her identity and she has ability to pay with a voucher and no criminal background, why would you deny her? 

DENY DENY DENY!

I'm going to ask the attorney how much discretion I have in this matter, ie, can I deny one tenant and permit another tenant, based on the one unit having wood floors and another unit having more resilient tile floors?

I like cash flow and yearly high performance numbers from 'linear' markets, but I cannot deny the historical performance of SoCal properties.The reality is that by holding on to CA properties long term, it will appreciate.

They requested the landlord do a walk-through of the unit prior to turning over the keys and was denied.  

You only have to worry if it can appear you're using a rule to deny someone who is a protected class.  

The landlord stated that they denied them because of their background check.

Indeed to reiterate indeed i've stated that i want to be especially more picky who i let in to see my duplex house(i live in) than even my other own properties. though can totally fathom todays litigious america where many a professional would never aknowledge a 'less than arm's length' potential transaction for what it is; deny everything.

Call them your wife, her kid, whatever - come apply when she gets to the country.And I think it's really important to stick to your criteria, and never be swayed away from your criteria because someone is promising to throw cash at you, so you'll ignore your criteria.If your criteria says someone doesn't qualify whose income is half the rent, then deny him. 

We go denied due to "wear and tear" we are still fighting that.