Well basically Hagerty are wrong on both points. On the Hagerty website it even has a link to the UK government guidance and that Goverment guidance says:
"Most vehicles manufactured or first registered over 40 years ago will, as of 20 May 2018, be exempt from periodic testing unless they have been substantially changed"
Further down the goverment document it says:
"From 20 May 2018, at the point of taxing a vehicle, the vehicle keeper can declare their vehicle exempt from MOT if it was constructed more than 40 years ago."
The government guidance also says the criteria for substancial change such as axles etc does not cover motorcycles, but further down motorcycles are covered for other things. So it does effect motorcycles, but not as much as cars.
See:
https://assets.publishing.service.g...ical-interest-substantial-change-guidance.pdf