Joel, I think you’re misunderstanding this passage.
The contrast with other polities in the sentence in Lysias 2.17 that follows ἥ τε γὰρ ἀρχὴ τοῦ ἐκείνων βίου δικαίᾱ and precedes the sentence in question doesn’t refer to changes of government or the expulsion of previous rulers in those other polities – it refers to ethnic cleansing: the Athenians are autochthonous, whereas in other polities, the populations had unjustly expelled the previous inhabitants.
πολλὰ μὲν ὑπῆρχε τοῖς ἡμετέροις προγόνοις μιᾷ γνώμῃ χρωμένοις περὶ τοῦ δικαίου διαμάχεσθαι: ἥ τε γὰρ ἀρχὴ τοῦ βίου δικαία: οὐ γάρ, ὥσπερ οἱ πολλοί, πανταχόθεν συνειλεγμένοι καὶ ἑτέρους ἐκβαλόντες τὴν ἀλλοτρίαν ᾤκησαν, ἀλλ᾽ αὐτόχθονες ὄντες τὴν αὐτὴν ἐκέκτηντο μητέρα καὶ πατρίδα.
“Unlike the majority [of populations], who had been gathered together from all over, and who expelled other people [who were living there] and settled land that was not their own [τὴν ἀλλοτρίαν], [our ancestors] were authochthonous and [continuously] possessed the same motherland/fatherland.”
Leaving this out (if that’s what 46 Stories did) does leave the sense of ἥ τε γὰρ ἀρχὴ τοῦ βίου δικαία somewhat puzzling, but it seems to mean that Athenian life did not begin with the injustice of ethnic cleansing. That really has no bearing on what follows in 2.18 – the point of pride that the Athenians expelled their previous rulers and chose a democratic form of government.
Thus, in 2.18, Lysias is not contrasting “their own rulers” vs. “rulers of foreign polities” in using the reflexive pronoun σφίσιν αὐτοῖς. Both in Lysias and in the simplified version, the reflexive pronoun, either σφίσιν αὐτοῖς or the alternative ἑαυτοῖς, merely refers to the subject of the sentence. That’s the essential function of reflexive pronouns. See Smyth 1218:
- Direct Reflexives.—The reflexive pronouns are used directly when they refer to the chief word (usually the subject) of the sentence or clause in which they stand.
““γνῶθι σεαυτόν” learn to know thyself” P. Charm. 164e, ““σφάττει ἑαυτήν” she kills herself” X. C. 7.3.14, καθ᾽ ἑαυτοὺς βουλευσάμενοι τὰ ὅπλα παρέδοσαν καὶ σφᾶς αὐτούς after deliberating apart by themselves they surrendered their arms and themselves (their persons) T. 4.38. Less commonly the reference is to the object, which often stands in a prominent place: ““τοὺς δὲ περιοίκους ἀφῆκεν ἐπὶ τὰ_ς ἑαυτῶν πόλεις” but the perioeci he dismissed to their own cities” X. H. 6.5.21.
http://www.perseus.tufts.edu/hopper/text?doc=Smyth+grammar+1218&fromdoc=Perseus%3Atext%3A1999.04.0007
See also CGCG 29.16, 29.17.