Yes, the restrictions for the previously restricted TOCs (GWR, LNER, XC & Avanti) clearly now state that leisure travel is deemed acceptable again, provided it is being undertaken in accordance with the government guidance.
The government guidance is to consider other forms of transport before going by train, so for those Safeguarded Priv holders who are making a longer journey, who don't have access to a car, the train is the only sensible option.
As with all other passengers, such Priv holders are asked to make a reservation on their intended train (and in the case of LNER it's still mandatory). However there is a request only to get reservations an hour before travel, to ensure that "ordinary" passengers aren't prevented from boarding.
A bit of an unreasonable request IMO but heyho... At least it's not an instruction!