It's a myth. There is no premium. The only tickets that aren't valid on HS1 are those routed "Not HS1", it's no different to any other route in the country in that providing it's a permitted route then any appropriate ticket is valid on it, in accordance with the usual rules.
There are no tickets routed "Not HS1" as far north as Sheffield. The cheaper fares to avoid HS1 are not available this far North, only in the South East area, in which case a small supplement is payable. It's not an issue at all from places like Sheffield as there is no cheaper "Not HS1" option available.
The DfT are to blame for this myth, as I understand it was either their idea or they would have approved it (I'm not sure which) to have the confusing "Plus High Speed" routeing. There should be no such routeing and all tickets that include High Speed should simply be re-routed "Any Permitted" as with any other route. I did hear on the grapevine there were plans to do this, I am not sure if it's still the case. It causes so much confusion as gateline staff sometimes give people hassle incorrectly and some passengers think that there is a premium to pay when there isn't. SET's poor publicity must also take some of the blame.