If Paul wanted to convey the idea of "freed," then he would have used a form of the Greek verb ἐλευθερόω, which occurs twice in this immediate chapter (Rom 6:18 and Rom 6:22), where Paul in fact makes the explicit allusion of being "freed from sin." In Rom 6:7 however Paul used a different Greek verb and for specific purpose.
The Greek verb is δικαιόω or "justified" which is the 3rd person perfect passive indicative, which only occurs in two other passages of the Christian New Testament in conjunction with the Greek preposition ἀπό (by, or from).
Matthew 11:19 (NASB)
19 The Son of Man came eating and drinking, and they say, ‘Behold, a gluttonous man and a drunkard, a friend of tax collectors and sinners!’ Yet wisdom is vindicated by her deeds.”
Luke 7:35 (NASB)
35 Yet wisdom is vindicated by all her children.”
The Greek perfect can be translated in the present tense as the above translations indicate. If we applied this same translation of that same verb-preposition construct (δικαιόω + ἀπό) now used by Paul, then Romans 6:7 would read as follows.
Romans 6:7 (Alternate 1)
7 For he who has died is vindicated by sin.
The idea is not that the dead person is exonerated, but that dead person is "done justice" by sin. For example, wisdom is "done justice" by her deeds (Mt 11:19), or wisdom is "done justice" by her children (Lk 7:35). So in this passage, the dead person is "done justice" by sin.
Romans 6:7 (Alternate 2)
7 For he who has died is "done justice" by sin.
Or to put it another way, the wages of sin is death (Rom 6:23). If Paul had otherwise wanted to convey the explicit idea of "freed," then he would have used a form of the Greek verb ἐλευθερόω, which he uses several verses later (Rom 6:18 and Rom 6:22) in explicit reference to being "freed from sin."