Case study: 2nd cousin match not detected

AncestryDNA
    - correctly detected sibling match between brother & sister
    - correctly detected match between 2nd cousin & 3rd cousin
    - does NOT show either brother or sister as related to either cousin

FamilyTreeDNA
    - does NOT show either brother or sister as related to 2nd cousin

So I downloaded raw data (except 3rd cousin's on her own Ancestry account), and uploaded to GEDmatch as follows: 
  
      A289999      George    -- 2nd cousin
A354893      Nancy     -- me
A578881      Jay          -- my brother



Questions:

Possible causes:
    - my own version of "hoosier daddy", or granddaddy in my case
    - hit 1% odds of missing 2nd cousin match detection 

- what GEDmatch tools should I use, and what results would be 2nd cousin match?

- if GEDmatch can't detect 2nd cousin match to either my brother or me, does that also prove that relationship doesn't exist?  or just that relationship undetectable, like 3rd cousin example here? ...