Two passages from the Scholia to Euripides’ Medea explain why Euripides told the story he did and what the ‘real’ facts were behind it.

Schol. B ad. Eur. Med. 9.1-11

“There’s a story from the philosophers that is much repeated—one Parmeniskos also offers—that Euripides changed the murder of the children to Medea because he accepted five talents from the Korinthians. [He claims] that the children of Medea were killed by the Korinthians because they were angry over her ruling the city and they wanted there to be an end of her ruling in Korinth, because it was her paternal [right]. For this reason he changed the [responsibility] to Medea. Hippus presents [accounts] about her residency in Korinth, as does Hellanikos. Eumelos and Simonides report that Medeia ruled Korinth. In his work called On Isthmian Affairs, Mousaios reports that Medeia was immortal, and he explains this also in his work on The Festivals of Hera Akraia.”

πολυάϊκός τις λόγος φέρεται τῶν φιλοσόφων, ὃν καὶ Παρμενίσκος ἐκτίθησιν, ὡς ἄρα πέντε τάλαντα λαβὼν παρὰ Κορινθίων Εὐριπίδης μεταγάγοι τὴν σφαγὴν τῶν παίδων ἐπὶ τὴν Μήδειαν. ἀποσφαγῆναι γὰρ τοὺς παῖδας Μηδείας ὑπὸ Κορινθίων παροξυνθέντων ἐπὶ τῷ βασιλεύειν αὐτὴν θέλειν διὰ τὸ τὴν Κόρινθον πατρῴαν αὐτῆς λῆξιν εἶναι· ὃ μετήγαγεν ἐπὶ Μήδειαν. περὶ δὲ τῆς εἰς Κόρινθον μετοικήσεως ῞Ιππυς [frg. 3] ἐκτίθεται καὶ ῾Ελλάνικος [frg. 34]. ὅτι δὲ βεβασίλευκε τῆς Κορίνθου ἡ Μήδεια, Εὔμηλος [frg. 3] ἱστορεῖ καὶ Σιμωνίδης [frg. 48]· ὅτι δὲ καὶ ἀθάνατος ἦν ἡ Μήδεια, Μουσαῖος ἐν τῷ περὶ ᾿Ισθμίων [FHG IV p. 518a] ἱστορεῖ, ἅμα καὶ περὶ τῶν τῆς ᾿Ακραίας ῞Ηρας ἑορτῶν ἐκτιθείς: —B

Schol. B ad Eur. Med. 264.1-11

“Parmeniskos writes the following for this line: “Because the Korinthian women did not want to be ruled by a barbaric, potion-pouring woman, they conspired against her and [planned] to kill her children, seven boys and seven girls. [Euripides says that she only had two]. They fled, pursued, into the temple of Hera Akraia and they stayed there. But even then the Korinthians did not hold back: they slaughtered all of them at the altar. Then a plague fell over the city, and many bodies were perishing because of a sickness. They received an oracle that the god must be propitiated for the hunt of Medeia’s children.  This is why each year during the appointed time seven girls and boys from the noblest families return to the precinct of the goddess and appease their rage—and the anger of the goddess on their behalf—with sacrifices.”

Παρμενίσκος γράφει κατὰ λέξιν οὕτως· ‘ταῖς δὲ Κορινθίαις οὐ βουλομέναις ὑπὸ βαρβάρου καὶ φαρμακίδος γυναικὸς ἄρχεσθαι αὐτῇ τε ἐπιβουλεῦσαι καὶ τὰ τέκνα αὐτῆς ἀνελεῖν, ἑπτὰ μὲν ἄρσενα, ἑπτὰ δὲ θήλεα. [Εὐριπίδης δὲ δυσὶ μόνοις φησὶν αὐτὴν κεχρῆσθαι.] ταῦτα δὲ διωκόμενα καταφυγεῖν εἰς τὸ τῆς ᾿Ακραίας ῞Ηρας ἱερὸν καὶ ἐπὶ τὸ ἱερὸν καθίσαι. Κορινθίους δὲ αὐτῶν οὐδὲ οὕτως ἀπέχεσθαι, ἀλλ’ ἐπὶ τοῦ βωμοῦ πάντα ταῦτα ἀποσφάξαι. λοιμοῦ δὲ γενομένου εἰς τὴν πόλιν πολλὰ σώματα ὑπὸ τῆς νόσου διαφθείρεσθαι. μαντευομένοις δὲ αὐτοῖς χρησμῳδῆσαι τὸν θεὸν ἱλάσκεσθαι τὸ τῶν Μηδείας τέκνων ἄγος. ὅθεν Κορινθίοις μέχρι τῶν καιρῶν τῶν καθ’ ἡμᾶς καθ’ ἕκαστον ἐνιαυτὸν ἑπτὰ κούρους καὶ ἑπτὰ κούρας τῶν ἐπισημοτάτων ἀνδρῶν ἐναπενιαυτίζειν ἐν τῷ τῆς θεᾶς τεμένει καὶ μετὰ θυσιῶν ἱλάσκεσθαι τὴν ἐκείνων μῆνιν  καὶ τὴν δι’ ἐκείνους γενομένην τῆς θεᾶς ὀργήν’.