Should one know verses that definitely refer to the "house" as a brothel, one would need some provenance on those particular verses to establish them as part of the original rather than verses that were added later by someone who assumed (as most people do) that "The House of the Rising Sun" was a brothel rather than a prison.
The following verses, all of which "definitely refer to the 'house' as a brothel,"
Beware the red light out in front
An' the pictures on the wall,
An' yellow gals dressed in purple shoes
Without no clothes at all.
Shun the red light an' flowin' bowl,
Beware of too much drink,
Them whores will take an' lead you on
To hell's eternal brink.
There is a house in New Orleans,
They call it the Rising Sun,
An' when you want your pecker spoilt
That's where you get it done.
They drink all day an' fuck all night
Until your money's gone;
They kick you ass out in the street
When the second shift comes on.
are found in Vance Randolph and G. Legman, Roll Me in Your Arms: "Unprintable" Ozark Folksongs and Folklore, Volume I, Folksongs and Music. Fayetteville: UAR Press, 1992, p 252.
The first two of these stanzas were collected "from a lady in Benton County, Arkansas, November 6, 1949. She heard it sung by her brothers, about 1920, with several 'nasty' verses which she could not remember."
The last two stanzas were "Sung by Mr. R. S., Joplin, Missouri, March 19, 1950. He says that similar verses were sung by miners around Joplin as long ago as 1905."
In contrast, the better known versions date from the 1930s, as outlined in earlier messages here (see especially the message from Stewie,13 Nov 02 - 01:53 AM). Since several of the earliest were commercial recordings, there might well have been some censorship of "explicit lyrics" and some padding of the song with extraneous ("rounder") verses to make up lost space.
The verses above seem to me to have about as good a provenance as you're going to get. The claimed dates place them among the earliest. "Girl" versions (necessary for the women's prison idea) and "ball-and-chain" verses seem to have come later.
This places the burden of proof with those who think the HORS might not be a brothel. The prison idea can be dismissed until new information to the contrary appears.