I hope I understand this all, although one thing is not clear. Do you both agree on the dob of Wilhelm Bolte (1829)?
case 1 (yours): father born 1806, died 1839; mother born 1806, died Chicago 1878
case 2 (hers): father born about 1800, died 1865; mother born about 1800, died Iowa 1865
One big problem with case 2 is the fact that the husband dies in Germany in 1865, while his wife dies the same year (earlier? later?) in the U.S. This is not impossible, but if your cousin refuses to share her 'proof' of this, I wouldn't belief her tree more than yours.
Even if there were 2 John Boltes both married to a certain Anna Jungesblut, how big are the chances that this 2 Annas migrate to the U.S. to different states to die there while husbands John passed away in Germany?
The base line of both stories is the same, but it seems you both use different facts. Very bizarre, but stick to your story if she provides no proof of all she believes to be the truth.