The account is based on proven facts and good reasoning?
Historical truth is often tainted by the perceptions and biases of the writer which is why Historical truths are so hard to come by. For this reason historians rather focus of Historical validity.
A Historical account that is valid is one that is based on proven facts usually drawn from multiple sources if possible. Also the historian compiling this account must use good reasoning such that other historians looking at the material can deem the account logical.