Short answer:

The world of naval resupply changes dramatically with coal; in the age of sail a ship could find much of what it might need for ordinary operations locally. Naval steam boilers required high quality thermal coal from some mined source, it was not available for purchase, barter or confiscation from pre-industrial peoples.

Coal was obtained from one's own colliers which accompanied the fleet, or coaling stations-- there were no indigenous stocks of naval coal. Food is abundant and had been bartered for since the days of Captain Cook. The specific incident you're referring to occurs in 1914, during wartime.

So there's no single answer without a "who, where, when" of specificity.

Discussion:

Keegan is here referring to the early days of World War I, where the German East Asia Squadron, which had been based in Tsingtao (undefendable, with Japan entering the war on the Allied side), begins an epic voyage across the Pacific. At this point, all the world naval powers have coaling stations around the world, but the danger for the German fleet was that their Pacific stations would very quickly be seized (they were).

So Admiral von Spee was trying to get across the Pacific, gather supplies, raid British and French commerce. His fleet had its own supply vessels and colliers, and when you have reference to his ships "coaling", they are loading coal either from the colliers or from a coaling station. The German fleet did have a clever bit of skullduggery where they planned to obtain coal and food from French outposts, by claiming to be French vessels, and one source suggests that they paid in gold for this -- but not to indigenous islanders, rather to other Europeans. von Spee also had a plan to seize French stocks of coal by force, but this plan didn't work out. The German fleet makes it across the Pacific, defeats some British forces in Chile, sails into the South Atlantic, gets their necessary coal from a captured British collier, and then in December 1914 von Spee unwisely decides to raid the British station at Stanley, on the Falkland Islands. A superior British fleet catches them, and only two of the German ships escape destruction.

None of that is particularly relevant to earlier first encounters with Pacific islanders. Food was in abundance in the Pacific -- Captain Cook describes bartering for pigs and coconuts with various trinkets, such as nails and bits of glass -- and also has accounts of disturbances resulting from disputed transactions. Terms of trade changed with season, supply and experience. Here's Cook's account of provisioning in Tahiti -- note the change even during the time of his visit.

For the first two Months we were at this Island the Natives supplied us with as much Bread fruit, Cocoa Nuts, etc., as we could well dispence with, and now and then a few Hogs, but of these hardly sufficient to give the Ship's company one and sometimes two fresh Meals a week. As to Fowls, I did not see above 3 dozen upon the whole Island, and fish they seldom would part with; but during the last Month we got little refreshment of any sort. The detaining of their Canoes broke off Trade at that time, and it never after was begun again with any Spirit. However, it was not wholy owing to this, but to a Scarcity. The Season for Bread fruit was wholy over, and what other Fruits they had were hardly sufficient for themselves; at least, they did not care to part with them. All sorts of Fruits we purchased with Beads and Nails, not less than 40-penny, for a nail under that size was of no value; but we could not get a Hog above 10 or 12 pounds weight for anything less than a Hatchet, not but that they set great value upon Spike Nails; but, as this was an Article many in the Ship are provided with, the Women soon found a much easier way at coming at them than by bringing Provisions. Our Traffick with this people was carried on with as much Order as in the best regulated Market in Europe. It was managed ashore chiefly by Mr. Banks, who took uncommon Pains to procure from the Natives every kind of refreshment that was to be got. Axes, Hatchets, Spikes, large Nails, looking Glasses, Knives, and Beads are all highly valued by this People, and nothing more is wanting to Traffick with them for everything they have to dispose of. They are likewise very fond of fine Linnen Cloth, both White and Printed, but an Axe worth half a Crown will fetch more than a Piece of Cloth worth Twenty Shillings.

Note the "Mr. Banks" mentioned here is the celebrated naturalist Joseph Banks.

So there's the specific story you're asking about -- von Spee and the situation of his coal dependent fleet at the outbreak of the First World War. And then there's a much longer story of European naval expeditions in earlier centuries. The legal status of Pacific islands changes during this period, as does their experience with Europeans, so you have to ask "which naval expedition, resupplying where, when?" to speak accurately about these operations.

See:

Pacific Strife, by Kees Van Dijk, Amsterdam University Press, Amsterdam, 2015.

Maurer, John H. “FUEL AND THE BATTLE FLEET: COAL, OIL, AND AMERICAN NAVAL STRATEGY, 1898-1925.” Naval War College Review, vol. 34, no. 6, 1981, pp. 60–77.

Anne Salmond. The Trial of the Cannibal Dog: The Remarkable Story of Captain Cook’s Encounters in the South Seas. New Haven: Yale University Press, 2003.

DYE, THOMAS S. “Gift Exchange and Interpretations of Captain Cook in the Traditional Kingdoms of the Hawaiian Islands.” The Journal of Pacific History, vol. 46, no. 3, 2011, pp. 275–292.

Cook, James; WJL Wharton ed. "Captain Cook's Journal" [1893 edition]

Bennett, Geoffrey. "Coronel and the Falklands" [1962]