GT - good points.
There seems to be some confusion at times about 'public land' - invariably Shire or Council land. War Memorials are usually covered by Shires and Councils, unless of course it is covered under trust or held in perpetuity by a Shire or Council on behalf of donated land- then it could be private land, held in trust for the public. Shire and Council land, including public parks and the such, are all covered under various by-laws of each state/territory Local Government Acts. There are by-laws that usually PROHIBIT digging, removal of soils/rocks etc (including for example the removal of worms believe it or not, sea-weed as well). There are also 'defacing' laws for any PROPERTY, which includes land, 'annoyance' laws, which is a matter of perception - e.g. a Shire/Council worker finds an act 'annoying' under a by-law (true!!).
All these acts on Shire/Council land are unlawful without permission - and that includes digging. Some people get permission, some are pushing their luck. I often quote the interstate idiot who detected and dug up parts of the footy oval at Maryborough Vic and was fined and used 'but I have a Miners right' as a defence. Survey says - bumbow.
Permission has been granted to detect around several memorials in the past. A couple of times to find 'lost' medals after ANZAC Day (at the request of local RSLs), to assist in archeological digs and the like.
'Public Land' has an awful sound - some people think its a free for all. Most Shires/Councils are pretty flexible but there will come a tipping point, as has happened already, where they will crack-down when the invisible line is crossed.