The assumption which has been made is that "in chorus" is the singer's (or a previous singer's) almost sensible substitution for a phrase which he misheard or did not understand. The surmise that the original phrase was "ink horn" is made on the basis:

1. that we need something which fits the extended metaphor (this sort of metaphor is quite common in traditional song but it's not often so elaborate) which entails:

a/ extemely large size and b/ a writing implement

2. that the original should sound at least a little bit like "in chorus"