Can DNA testing cause confusion as well as solve puzzles?

Question

Five men tested Y111

Testee      MRCA              Earliest Common ancestor   Genetic Distance from

Jay            Leonard/1764      John/1670                       GD-1 from Perrin

Jay            William II/1657    William II/1657                 GD-1 from  Charles, 

Jay            William II/1657    William II/1657                 GD-2  from  myself

Myself      Stephen 1756       William II/1657                GD-2  from Charles

Charles      Stephen 1756       William II/1657               GD-3  from myself

Problem Charles and I  share Stephen b. 1756 as a MRCA (his 3^rd my 4^th ggf) yet we are at a GD of 3 at Y111, and a GD -2 at Y37 and Y67. Our y67 DYS are one step apart at two fast mutators DYS 460 and CDYb.

Yet Charles is genetically closer (GD-1) to Jay and Perrin with whom their most recent common ancestor is  Col William Farrar born 1657. He is at a GD-1 to Jay and a GD-2 to Perrin (at Y111).

Charles is my 4^th cousin 1 x removed. Y37/67 GD-2, Y111 GD-3 (per paper and auDNA)

I am certain of our genealogical paper trail, however genetically (in the form of GD) Charles is closer (GD-1) to Jay whose common ancestor is Col Wm II born 1627.

It is believed that my DNA is the modal for the Farrar of Virginia group, save for CDYb which is has a high mutation rate. The Farrar of Virginia group claim as ancestor William who migrated to Jamestown aboard the Neptune in 1618.

There is another who is a perfect Y67 match to me. Per paper trail our common ancestor is William III, b 1682.  He does not match me with auDNA (he would be a 6^th or 7^th cousin), However he is 3^rd through 5^th cousin with three persons, whose MRCA is Richard Farrar born 1750. These people are not auDNA matches with me, our common ancestor would be my 4^th great grandfather.  Those who share 4^th great grandparents are 5^th cousins  However my 4^th ggf is their  5^th (aka 6^th cousin)

5^th cousins  do show up as auDNA matches. Can there be exceptions when they don’t?

Charles  who is at a GD-3 to me at Y111, shows up as my 4^th cousin once removed (auDNA) and genealogically we share Stephen Farrar born 1756 as an ancestor

Yet three(paper) 5th cousins don’t show up as auDNA, mttches to me, while a 7^th cousin once removed shows up as a 3^rd-5^th cousin to these 5^th cousins

It is possible that some or most of these paper trails are incorrect, (I suspect an NPE between Farrar cousins) in one case. My Y67 GD-0 who registers as a 3-5^th cousin with my three (paper) 5^th cousins, who do not register with me as auDNA 5^th cousins.

Can I take auDNA to the bank?

And what of persons who are at a GD of 1, yet their common ancestor was born 1657.

And a person whose common ancestor is a 3^rd an 4^th ggf, yet are at a GD-3 at Y111 with me, and   is a GD-1 with someone  whose MRCA was born 1657.

It makes me question everything when I am GD-3 and a 4^th cousin once removed with a man whose common ancestor was born 1756, yet that same person is at a GD-1 with a man whose MRCA was born 1657.

Then there is James who, paper wise, shares with me a common ancestor born 1682, is Y67/67, has no auDNA match with me, but is an 3^rd-5^th cousin with three people whose ancestor was a brother to my 4^th ggf (my 6th^h cousins)