"Untrue" is not the same as lying.
I make factual errors all the time, and most are NOT lies. Some are due to carelessness, such as not double-checking, some are due to receiving incorrect information from others, and some are due to misinterpreting text because English is inherently vague and/or one context can be mistaken for another.
Work-related emails are often terse and assume prior work knowledge, domain lingo, and/or context.
This is "Office Life 101", I shouldn't have to explain it. Normal people know all this.