It's possible. However the Heaphy Track is one of the most popular walks in NZ, so one would think that if there were Kokako still there then they would be reported much more frequently. (There is a map in this article
Bird call raises hopes of finding the elusive kōkako - which I think is the report your BirdGuides link is discussing - which has a string of potential reports along the track, which is interesting but to me also makes it seem less likely because if they are being seen or heard along the length of the track then confirmation should have come long ago).
Also Kaka, Tui, and Bellbird can all make similar calls. In this BirdingNZ thread
S I Kokako - BirdingNZ.net there is a photo on the last page of what a juvenile Bellbird looks like - blue-grey plumage with yellow at the gape; anyone who birds knows that one species can be mistaken for another in the field, even if they can be easily told apart from photos or with clear views, and
especially this can happen if the person is specifically looking for the species. (Side-note, the posts there also mention the volcano which erupted in Tonga last week, which could be heard in NZ. I heard it but thought it was fireworks because I didn't know there was a volcano erupting in Tonga!)
So, in summary, I hope they are still out there but it's a smaller than average chance. If they are still there then they will be so close to extinction, and quite possibly with only males left. (Females are killed on the nest by possums and other predators; in the North Island, mainland populations of Kokako typically end up being mostly male unless the areas are heavily trapped to keep down predator numbers).