Following the link https://wiki.jenkins.io/display/JENKINS/Remote+access+API to remotly trigger a job, I am seeing:

'Access denied. oleksandr-kushchak is missing the Overall/Read permission.'

We are using a matrix based authorisation, and oleksandr-kushchak is a part of admin group who has admin access.
When I add oleksandr-kushchak separately to the matrix and give Overall/Read permission everything works fine.

The workaround for now is to add a user to the matrix but it would be nice to see this working.