People make this mistake every day with common infections that are not acts of bioterrorism. This key difference in the case of bioterrorism is that we will have huge numbers of casualties in short order instead of the occasional "oops".
Based on what I've read an initial act of bioterrorism may be misdiagnosed until it is "figured out" by volume of victims, cultures, tests, etc. By then victims of the initial episode may have developed more serious symptoms.