I suspect that 3 is true if you look at the educational requirements. Sandhurst requires 72 UCAS points which is roughly equivalent to 3 A levels. That means the people that leave education with GCSEs and go on to become sparkies, plumbers etc. effectively don't count as they are not eligible.If 1) a state comp is as good as public school and 2) the army wants the best people then 3) the ratio would match the general population. 3 isn’t true so either or both of 1 and 2 can’t be true.
Compare the number of school leavers with 3 decent A levels from state and public schools and I reckon they would be fairly similar.