If it is Potentilla, the only species with three leaflets is Potentilla indica. It might be Fragaria (strawberry), but that does not appear to have been naturalised in either NSW or Victoria.
I was thinking Potentilla (Fragaria) vesca which is low growing. Described in Richardson et. al. Weeds of the South-East. Also Mapperley in Telopea 9(4): 2002 "14. Fragaria vesca L. = Potentilla vesca (L.) Scop. Notes: Cultivars of this are the ‘alpine’ strawberries of patisserie. Diploid. Cultivated in Australia (material apparently brought with the First Fleet, 1788), this North Temperate species is naturalized in New Zealand." I will have to see if I can catch it in flower: yellow for P. indica and white for P. vesca.
I have found a key in A.R. Bean, Muelleria 33: 75–83 4 Epicalyx segments 3–5-lobed; petals yellow; hairs on lower leaf surface confined to veins .................................. *Potentilla indica 4: Epicalyx segments entire; petals white; hairs distributed all over lower leaf surface .................................................................................. 5 5 Achenes 1.2–1.3 mm long; petals 5–8 mm long; inflorescence branched only near apex ......................................... *Fragaria vesca The leaves have hairs on the underside, similar to the edible strawberry in my garden. The article also seems to put the name back to Fragaria.
I checked in APNI. The tick for Potentilla vesca still holds. They cite the reference you mention. The Council of Heads of Australian Herbaria (CHAH) has either decided not to go with AR Bean's work or they have not yet got round to discussing it.
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