It does not burn easily but once aluminum has ignited it can continue to burn under normal atmospheric conditions, especially if it begins to melt and boil.
Sparks are hotter than 3073°C, but usually they don't ignite aluminium either--there not being enough aluminium vapour to sustain the reaction.
I've done what you said and googled, but have not found a case that indicates non-dust aluminium was burning.
https://www.readingeagle.com/2022/04/19/reamstown-fire-alumi... : Looks like a dust fire. Easily extinguished. Does not sound like any solid or molten aluminium was burning.
https://dailyvoice.com/pennsylvania/lancaster/news/fire-brea... "The fire is believed to have started in the finishing area, where workers grind the aluminum castings"
https://www.fox43.com/article/news/local/fire-aluminum-found... no details
https://lancasteronline.com/news/local/fire-damages-east-coc... "not sure what caused the fire, which began near – but not in – a dust collection system at the plant."
https://www.abc4.com/news/fire-causes-400k-in-damages-to-ogd... "The fire was contained within an hour after crews arrived. No one was injured. Damages were mainly to the machinery and the foundry metal fabrication plant structure."
https://mix999fm.iheart.com/featured/murphy-sam-jodi/content...
https://news.yahoo.com/fire-boose-aluminum-foundry-lancaster... (Video shows normal flames, not from a metal fire.)
It burned until there was no more silver color metal left, leaving just the copper wire leads. I assume it was aluminum, I think steel would be harder to burn.
I do remember unplugging it during the fire, but it didn't take very long to burn, so I might have done it after it was over.
Magnesium can be set alight even when multiple cm in thickness [1], and lighting up thin strips is much more spectacular[2]. You can hold aluminium foil to a blow torch, what happens is it will melt and oxidize, but not produce any flame or light whatsoever[2]. If aluminium foil doesn't do it, I don't see how a thicker sheet would do it. And all I've found confirms this. (BTW steel wool however does burn continuously. But I agree that a steel lamp base burning this way doesn't look feasible, either.)
[1] e.g. video on https://en.wikipedia.org/wiki/Magnesium [2] source: own experiments, and there will be videos from others
Since you say that it was thin, it must have been an alloy in either case. It seems Magnesium alloys need to be cast. I've got a laptop with a magnesium base which looks like sheet metal from the outside but when you open it up, on the inside it has all sorts of structures coming out of the "sheet", clearly confirming it was cast. I've never seen aluminium parts made that way, aluminium cast parts seem to always be relatively thick, not like sheet metal. Aluminium can be pressed, however (think beer cans), but then it doesn't have a fancy structure. I'm not a specialist in these matters in any way, but maybe this might give some further ideas.