People have been trying to make this claim for decades. See this case from 2003:

A jocular use of a form of the rhyme by a Southwest Airlines flight attendant, encouraging passengers to sit down so the plane could take off, led to a 2003 lawsuit charging the airline with intentional infliction of emotional distress and negligent infliction of emotional distress. Two versions of the rhyme were attested in court; both "Eeny meeny miny mo, Please sit down it's time to go" and "Pick a seat, it's time to go". The passengers in question were African American and stated that they were humiliated because of what they called the "racist history" of the rhyme. A jury returned a verdict in favor of Southwest and the plaintiffs' appeal was denied.

It seems that, at least for now, sanity has prevailed and any attempt at "BUT MUH HUNDREDS OF YEARS AGO" has been quashed.