Was the 14th Amendment never properly ratified?

I've just read a crazy claim that the 14th Amendment was never ratified.  To pass a constitutional amendment requires 3/4 of the states.  There were 37 states in 1866 when the amendment was proposed.  So 28 states had to approve it.  If 10 or more rejected it, then the 28 number wasn't reached.

The amendment was proposed on June 16, 1866.

New Jersey passed it on September 11, 1866 then rescinded it on February 20, 1868.

Oregon passed it on September 19, 1866 then rescinded it on October 16, 1868.

Ohio passed it on January 11, 1867 then rescinded it on January 13, 1868.

North Carolina rejected it on December 14, 1866 then approved it on July 4, 1868.

Louisiana rejected it on February 6, 1867 then approved it on July 9, 1868.

South Carolina rejected it on December 20, 1866 then approved it on July 9, 1868. 

Georgia rejected it on November 9, 1866 then approved it on July 21, 1868.

Virginia rejected it on January 9, 1867 then approved it on October 8, 1869.

Texas rejected it on October 27, 1866.

Delaware rejected it on February 8, 1867.

Maryland rejected it on March 23, 1867.

Kentucky rejected it on January 8, 1867.

Florida rejected it on December 6, 1866.

Alabama rejected it on December 7, 1866 and then approved it on July 13, 1868.

Arkansas rejected it on December 17, 1866 then approved it on April 6, 1868.

Mississippi initially ignored it and didn't ratify it until January 17, 1870.

California initially ignored it and didn't ratify it until May 6, 1959.

Just looking at the initial rejections and also counting those that didn't approve it by the end of 1867 and ignoring those who approved it and then rescinded, these states rejected or ignored it: Alabama, Arkansas, California, Delaware, Florida, Georgia, Kentucky, Louisiana, Maryland, Mississippi, North Carolina, South Carolina, Texas, Virginia.  That is 14.  

So only 23 states initially approved it.  Those states are:

Connecticut

New Hampshire

Tennessee

New Jersey

Oregon

Vermont 

New York

Ohio

Illinois

West Virginia

Michigan

Minnesota

Kansas

Maine

Nevada

Indiana

Missouri

Pennsylvania

Rhode Island

Wisconsin

Massachusetts

Nebraska

Iowa

So they were 5 states short.

Hmm, I think we are on to something suspicious here.   Of course there is more to the story.  To be continued...

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Part 2:  
In early 1868, Ohio and New Jersey rescinded their ratifications.  Their reasoning was that the 14th Amendment guaranteed black people rights but discriminated against former Confederates.  There was a question as to whether they could rescind, but assume that they did.  Now the 14th Amendment only had 21 states supporting it.

But then the reversals starting rolling in. 
Arkansas in April 1868.
Florida in June 1868.
And in July 1868, North Carolina, South Carolina, Louisiana, Alabama and Georgia all changed their minds and ratified it. 

So the magic number of 28 was reached on July 21, 1868.

But why did the 7 states change their minds?