Not sure what people are upset about with "political" answers... Some men are married to other men. If 'she' being NOT one of the male partners is going to get the other person's partner this statement would be correct.
If a co-worker of mine is going out to the waiting room to get the husband of my male patient this is completely a correct statement.
i.e. Doctor asks "He is dying. Where is his family?" My reply "She is going to find his husband." (She being another nurse)
The reason it is her in this sentence is that without other context clues to suggest otherwise I. E. a conversation about someone, or a clarifying phrase, the convention is to assume su refers back to the subject. Since Ella is the subject, assume su is her. If it was usted, then your would be expected for su. Finally, it could be about él and then su would imply him. If there wasn't agreement in a stand-alone sentence, you would clarify in a supporting phrase.
Spanish uses 'a' before the direct object when the direct object is a person or pet. It is a pronoun use that has no translation into English but it IS required in espanol. So in this example the first 'a' is translated as 'to', as in (going to meet), in English. However, the second 'a' serves no purpose in English and is not translated. (But it is NOT optional is Spanish and it is wrong not to use it). See link, please, for more information. http://www.studyspanish.com/lessons/persa.htm
In a standalone sentence like this, it's reasonable to assume that "su" refers to the subject. If "Ella" = she, then "su" = her. But actually "su" could mean his, her, your or their, and, without context, there is no way of knowing which was intended. Duo should accept any of them.
I think "buscar" can mean "to find" in the sense of you don't know where the person or thing is, so you have to look for that person or thing. Whereas, "encontrar" can mean "to find" in the sense of you are not at the same place so you must go and meet up with that person. se buscar or buscarse is reflexive I believe. "Yo me busco la vida como puedo." for instance means "I sort out (or earn or make) a living for myself as (best as) I can." Perhaps that wasn't the best example as it is an expression, I put the implied meaning in parantheses. "Me busco una isla." is "I find myself an island." "Voy a buscarme una isla." which is "I am going to find myself an island." http://dictionary.reverso.net/spanish-english/buscarse
Will be "me busco en una isla" not "me busco a una isla", buscar could be to find or search... you know because of the context, "busco un libro" i search a book, "encuentro un libro" i find a book. And i will find myself at an island... is "voy a buscarme a mí mismo en una isla" because you don't know where are you ... but if you say "voy a encontrarme a mí mismo en una isla" i am going to find myself at an island... gotcha?
@ allintolearning I used "buscarme" without any references or knowledge; however, just now consulting Spanishdict I did find two instances. The first was shown in Collins Complete Spanish Electronic Dictionary: Ven a buscarme a la officina." Also: "Vais ir a buscarme a la estacion." shown in Valaquez Spanish and English Dictionary. The two instances were listed under verb transitive. Duolingo was possibly wrong in accepting it as a correct answer. Thank you for your reply and the links you provided.