Most definitely. At least that is always what I would recommend. A recent PR Week article suggests that trained spokespeople should be able to participate in a direct discussion with the media. If there is an ongoing close relationship between the spokesperson and the journalist, this can be great but if an ad hoc discussion then definitely not.
There at at least five reasons for a PR to be present in all media interviews:
1. The spokesperson doesn't understand the media as well as the PR does and may not be giving the journalist what they need
2. The PR should own the relationship with relevant journalists
3. The spokesperson is busy and is not always best at following up on actions discussed in the meeting
4. The PR is ultimately responsible for what is published and has no influence or ability to follow up if not present in an interview
5. The PR will not be able to help the spokesperson bridge to key messages if the discussion goes off track
Any experienced journalist should hopefully see PR as a resource and there to help and support the process rather than get in the way. If a journalist ever requests that the PR is not present, it should raise a flag that they might want to try and catch your spokesperson out.
But don’t feel you automatically have to sit in on every interview your spokesperson carries out.