The answer to your question is yes. Sort of. The problem is with terms and definitions. First a quick overview of the definitions of two terms - legend and myth (this is from my Introduction to Folklore that I use for my classes):

Legends – or Sagen as the profession often prefers – are generally short, single-episodic stories told chiefly in the daytime. More importantly, the teller intended the listener to believe the story. Legends often have horrible ending to underscore the story’s important message. Many of them are, after all, meant to be instructive, to serve as warnings in some way. These types of stories are not necessarily long-lived. Their point is to reinforce and prove the legitimacy of a belief. Nonetheless, some legends take on a traditional character, can become multi-episodic, and migrate over considerable spans of time and space.

People use the term "myth" awkwardly. In a European context, myths tend to be the artificial constructs of ancient and Classical-era priests or literate people who sought to weave folk traditions into a comprehensive whole. The exercise often had political purposes, designed to provide diverse people with a single set of beliefs and stories. By reconciling similar traditions, the shared culture of these groups could be seen as more important than the differences, justifying the central rule of the king and his priests. Myth is also a way of organizing and reconciling folk traditions, which by their nature can be contradictory and highly localized. Myth tends, however, to make gods of supernatural beings, giving those powerful entities a status – for modern readers – similar to the Judeo-Christian-Islamic God, even when this comparison is not justified. Of course, it is also important to point out that myths were stories that were told – and then written down – and they were different from religion itself. Many myths were simply the shared cultural inheritance of a group of people.

In general, the word myth is best set aside when discussing more recent folk traditions, recognizing its proper status as a literary genre. Nonetheless, ancient documents recording myths can assist in understanding the history of various stories and beliefs. The authors of these texts were, after all, the first folklorists, and they were the only ones coming close to practicing the craft at the time.

Some folklorists carelessly use the term myth to denote those legends that deal with a fantastic, remote time. This primal era saw the creation of many familiar things such as day and night, fire, animals, people, mountains, and all other aspects of the present world. Folklorists properly refer to these stories as etiological legends explaining the origin of things. Sometimes, however, people interchange etiological legends with the word myth. The problem with this is that “myth” can imply something that is inherently wrong, linked to “primitive” superstitious beliefs. When the term “myth” is used for the folklore of existing cultures or for the traditions that were viable only a generation or more ago, it can take on an insulting, derogatory tone. It is best to reserve the word “myth” for ancient and Classical-era texts.

So, if we accept that a myth is something that is written - removed a step from oral tradition - then we can understand that the tradition that remains oral and fluid can and probably would accommodate extraordinary circumstances with much the same vocabulary, characters, and belief system that was for found in the written text, assuming that the myths were not describing fossilized traditions and beliefs that were no longer current.

The way people usually accommodate remarkable circumstances is to interpret them with the beliefs they have available. Of course, people experience life in the past, so if something current would soon be described and interpreted in the past tense, but that process is much the same for the recent past -"Did you see what happened yesterday? Certainly that was supernatural being A interacting with Supernatural being B." - that sort of thing, but all in a recent past tense. This description of a recent event may or may not make the transition into the local oral tradition in a permanent way. Often these observations and interpretations last only for a while, or if they are longer lasting, they don't survive past those who observed the incident. Folklorists refer to this type of legend as a memorate. These are the stories we all tell about remarkable experiences we have had. They are rarely repeated by anyone other than ourselves and so they do not become part of the larger oral tradition, but sometimes they do, and these would then fold themselves into the larger body of folklore.

I hope that helps.

In a more strictly mechanical sense than what /u/itsallfolklore has said, though basically a reiteration of his comment, myth is and was written in the present tense all the time. The texts from which we receive "mythology" (a modern word that a Greek would not understand) are poems, plays, and anecdotes in larger verse or prose works. Quite frequently these are written in the present tense because that's a perfectly acceptable literary device.

Consider your reference to Actaeon. You say that "all Ancient Greeks knew, for example, that Acteon stumbled on Artemis and she turned him into a stag." First of all, the Greeks "knew" no such thing. The earliest mention of Actaeon, in Hesiod, has him rape Semele, whereupon Zeus has Artemis send her dogs after him. Later, Euripides has him get killed because he bragged he was a better hunter than Artemis. Only with Callimachus, and especially a Roman poet, Ovid, does the familiar (to a modern reader) story of Actaeon's spying Artemis bathing first appear, centuries after the character's first appearance in literature.

Second, Ovid uses the present tense. Actaeon appears at Met., 3.138 and meets his end around a hundred lines later. Throughout the passage Ovid uses mostly the present tense, moving into the perfect and imperfect sometimes to describe the setting. Part of this is the so-called Latin "historical present," a common rhetorical device used here to describe Diana's undressing, the pursuit of the dogs, etc. But the telling of what we call "myths" in Greek literature was presented in all kinds of different forms. Perhaps most common in Homer--in which the characters are themselves acting out a myth--is the story within a story, in which a character relates the story of what some hero of the previous generation is said to have done. Those are in the perfect or imperfect, but are they really? What is the relationship of the characters to the stories they're telling? Much of our other "mythology" comes to us through tragedy, in which the myths are being literally acted out in front of the audience. There's no past tense here, nor is there a present, the action is now and the audience is supposed to consider what's happening on the stage. There are other cases that are more cut-and-dried. Pindar, for example, refers to Typhon's imprisonment under Aetna as happening right now, although he refers to the monster's birth in the perfect.

There was no orthodox canon of stories compiled somewhere into some official narrative, which means that these stories appear in whatever verbal tense the author transmitting them in his own work thinks is appropriate to the action.