This claim is generally made less about Standard American or General American and more about regional Appalachian dialects. Even this is a myth. 
<a href="http:&#x2F;&#x2F;itre.cis.upenn.edu&#x2F;~myl&#x2F;languagelog&#x2F;archives&#x2F;002699.html" rel="nofollow">http:&#x2F;&#x2F;itre.cis.upenn.edu&#x2F;~myl&#x2F;languagelog&#x2F;archives&#x2F;002699.h...</a>
<a href="http:&#x2F;&#x2F;lrc.ohio.edu&#x2F;lrcmedia&#x2F;Streaming&#x2F;lingCALL&#x2F;ling270&#x2F;myth9.pdf" rel="nofollow">http:&#x2F;&#x2F;lrc.ohio.edu&#x2F;lrcmedia&#x2F;Streaming&#x2F;lingCALL&#x2F;ling270&#x2F;myth...</a><p>English and American dialects both originated in (Shakespearean) Early Modern English, but both have changed over time, as languages do.