RE: I am perplexed with this result.  Taxable income is about $25K, after Standard deduction.  But there is no tax. 

Jeff's answer nailed this, the "perplexedness".  (BTW, When something is quote-unquoted, no need to change the spelling or grammar.)  

RE:  Was I wrong when I thought that the couple has to file the return?

@rbynakernailed this.

Two awesome nails.