The opening phrase that describes the wrong person
A phrase at the start of a sentence quietly borrows its subject from the main clause, which is how confident writers end up attributing an action to whatever happens to follow the comma.
Having reviewed your file, we have issued a refund.
An opening phrase built on a verb form has no subject of its own. It borrows one automatically from the main clause that follows, whoever or whatever that subject happens to be. So when the main clause names something that did not perform the action in the opener, the sentence claims something absurd, and it does so with flawless grammar and no warning signal. There are exactly two repairs: make the real doer the subject of the main clause, or expand the opening phrase into a full clause with a subject of its own.
This is not a learner error but a fluent-writer error, and it is everywhere in business email. It appears most often when the opener describes something a person did and the main clause is passive, so the only subject on offer is a document, a payment or a decision. Readers normally reconstruct the intended meaning, which is why the habit survives unchallenged, but for a moment the sentence says something ridiculous and attentive readers do notice. Compare the repairs above: the first and third lines supply the real doer as the subject of the main clause, while the second and fourth give the opening phrase a subject of its own. If neither repair is available to you, the shortened opener is simply the wrong structure for that sentence.