赞同曹老师的解答。that引导的是同位语从句，说明主语story的内容，为了保持句子平衡，that从句移至谓语动词goes之后。这里的goes是不及物动词，其汉语意思常根据主语的意思灵活翻译。以下解释摘自《韦氏高阶英汉双解词典》：

--- used to talk about a story, song, etc.（故事）发生情况；（曲调等的）唱，说。

I can't remember how the story goes. [=I can't remember what happens in the story] 我记不起这故事的情节了。

The story/rumor/legend goes that he left home poor and came back rich. 传说他离家时身无分文，之后衣锦还乡。

▲《牛津高阶英汉双解词典》也有类似解释。

(used esp in questions after how 尤用於疑问句中的how之後) (of a piece of music or writing) have a certain tune or wording （指一篇乐曲或文字）有某种基调或措辞: 

How does that song go? 那首歌是怎麽唱的?

The national anthem goes like this... 国歌是这样唱的...

I forget how the next line goes. 我忘记下一行是什麽了.

The story goes that she poisoned her husband / She poisoned her husband, or so the story goes, ie It is said that she poisoned him. 故事说她把丈夫毒死了. 

这里有同位语吗？ 我从没想过。语法咱也不精通。

首先go 可以是及物动词，也可以是不及物动词。

这里的go 相当于say, read 的意思

这就是个间接引语, 你可以假装它就是个直接宾语。怎么扯到同位语上去了？

整句意思相当于 It is said that William killed his wife.

或 Somebody says that William killed his wife. 

从这个角度再分析一下，可能对你有启发。

the story goes (that)…这是一种固定结构，在固定的结构中that+作story的同位语，但反过来又不能推导出that在其它结构中也可以作story的同位语。

The story goes that William killed his wife.    ✔

He told me the story that William killed his wife.    ✘