I don't know why the above comment has a -1. This is actually the reasoning behind the grammar, even though it may seem anti-gender equality. Speaking from living in Kenya, the culture is very male-dominated, and that transfers over to the language as well. So when you use the verb "to marry," it is used differently for a man or a woman.
ex: Rashidi ameoa na Esther - Rashidi has married Esther Esther ameolewa na Rashidi - Esther has been married to Rashidi
Based on the book I have on Tanzanian Swahili, this holds true for that dialect as well.
I think the difference in the Swahili is that the literal translation would be "married by" but in English that has the connotation of the person performing the service, the judge/priest/pastor/rabbi/etc. In the Swahili grammar, the woman has the action of marriage done to her by the man where as the man does the action of marriage. Neither of our English phrases, married or married to, carry that happening-to-me connotation. (Tonga, another Bantu language which I previously studied via tutoring and immersion, operates this way, and this is how my village father explained it to me after everyone laughed at me after I used the passive version while discussing a male.)
In English there isn't, but in Swahili there is, that's the thing. In English we can say either Esther married Rashidi, or Esther is married TO, Rashidi. Remember this is a Muslim majority culture where men marry women and they are subject to their husband. So in Swahili we must say Esther ameOLEWA na Rashidi, never Esther anaoa Rashidi. If the role is reversed we say Rashidi anaoa Esther.
Also, regardless of how the grammar works in the source language, the text should make sense and be natural in the target language. The meaning should be translated. For this situation, English speakers would either say "Esther has married Rashidi" or "Esther is married to Rashidi".
When you translate German Handschuhe into English, you say "gloves", not "Hand shoes". The latter may be more "accurate" in terms of conveying what is happening in the German language, but it's simply not what we say in English, so it's an incorrect translation.
If we're being really technical this sentence is passive voice so it translates as "be married," but in this case it really makes no difference, the point is the woman in this situation does not "marry" but is "married to" a man, "married by" a man, has "been married" to a man. It all basically means the same thing.
You have a point, but as you said this is what you 'expect' when you hear the words, or what the words mean to you, not necessarily what that means. In fact, you wouldn't need to say 'married by' to refer to the person doing the ceremony. First let's explain by defining "marry" as a verb(This is from Merriam-Webster). Marry: 1) a : to join in marriage according to law or custom b : to give in marriage "married his daughter to his partner's son" c : to take as spouse : wed "married the girl next door" d : to perform the ceremony of marriage for "a priest will marry them" e : to obtain by marriage "marry wealth" Definitions a, b, and especially d, show that 'marrying' isn't done specifically by the bride and groom. The sample sentence in d literally says "a priest will marry them." Obviously it is not saying that the priest is going to be a husband, or a bride to the (assumed) couple, but he is doing the act of legally joining them in marriage.
As for the word 'by' it's definition usually means something like near, or in this case through. by: 4a : through the agency or instrumentality of "a poem written by Keats," "death by firing squad," "taken by force," "happened by luck" b : born or begot of "had two sons by his first wife," "one child by her second husband" c : sired or borne by "having foals by champion race horses" Here a and b, refer more to this situation. And they basically lead to the conclusion that 'by' can refer to a creator, like a priest or judge in a marriage(coming from def a), or an object that is acted upon by another object(from def b). So, when we add 'by' as an adverb here, it doesn't specifically refer to the priest, it can be in reference to the (assumed) bride and groom. It is correct to say the groom was married 'by' the bride, and the bride 'by the groom. It's just not ordinarily said in this way.
Finally let's break down the Swahili equivalent to the verb marry: 'kuoa.' Don't think of this as misogyny, but in Swahili, brides do not 'marry' their husband. You do not say 'Esther anaoa Rashidi'(Esther is marrying Rashidi) You must say use the verb 'kuolewa,' which is passive voice of the word 'kuoa,' meaning "be married." So you say 'Esther ataolewa na Rashidi"(Esther will be married by Rashidi, or Esther will be married to Rashidi). So looking at all of these together, to translate using "married by," or "married to," makes very little difference, from a technical grammar standpoint.
However, there is something to be said about what is more recognizable in a language, and most people would probably think of "being married by" in a similar way that you did. So translating as "married to" is a more recognizable/better translation.
TL;DR They can be interchangeable, but saying "married to" would be a more preferable translation.