Here in the UK the current "general" thinking is that .270win is a good minimum consideration for boar. Frankly, I would never rule out even the 6.5x55 Swede (I've seen it used to take boar very efficiently) but the advice here is what it is and the Police know it.
Now, what is a .270win? it's a necked down .30-06 and actually fires similar bullet weights at similar (to near identical) velocities, but with better drag co-efficients. So the "leap" to .30-06 is neither massive nor illogical (i.e.you can use better suited "slow-heavies" in the old ought six)
What is a 300 win mag? ... Well, it may be a shortened-case .30 cal derivitive of the serious big game hunter's .375 Holland and Holland and it certainly looks the part but... in reality it's just the .30-06 with about 120yds more velocity at this end. that's to say it starts of with a higher muzzle velocity than the .30-06 but at 120 yds the 300's bullet is travelling at about the same speed as '06's does at the muzzle and from there on out they are equal (i.e. with the .30-06 velocity always trailing by about 120yds). The Police seem to worry greatly about the risk centre-fire rifle bullets pose at 3or 4 miles????

I'd say the diference between
3 or
4 miles and....
3miles +120yds or
4miles +120yds is entirely meaningless. In fact, if Police advice is that .270win is a recommended minimum then .300 win mag must be nearly perfect by their own admission, though maybe not quite as perfect as a decent 9.3
If there's a debate about conditioning for deer, there is NO debate, it's just a slightly ramped up .30-06 and surely better you have one rifle for deer AND boar rather than need an extra rifle just for boar.
The above has to be your thinking, but on your form just explain your good reason, which comes from such thinking in relation to what you wish to do.... et voila.... a reasoned approach which you can back up in interview, if needs be and which would make refusal on cartridge choice alone an unsustainable position should the need for a judicial review arise. I.M.H.O. that is.