A strict reading of this does indeed seem to permit any train the same day.The LNER website says: https://www.lner.co.uk/travel-information/leeds-timetable-changes/
It would appear there are no time restrictions as long as you travel on the same day.
I am not sure if I would try it, but there's no denying it says what it says.
In some circumstances e.g the 1745, one may find that the following train is subject to overcrowding as it carries both train loads of passengers. I would certainly feel justified in perhaps taking the second available train in circumstances where I couldn't be sure of an available unreserved seat. Especially as, if your train is cancelled, you lose your reservation.