It's a widespread myth that Lithium-Ion battery fires involve burning lithium. They do not contain any metallic lithium at all, the whole point is that they use lithium ions.
I tend to agree with you.
Do lithium-ion batteries contain lithium metal? I am not an expert, so I do not know the correct answer. I fly quadcopters which use lithium-ion batteries, so I am interested and have researched this subject extensively, and have not found a definitive answer.
Here is an example of conflicting information from Battery University:
BU-704: How to Transport Batteries (
https://batteryuniversity.com/learn/article/how_to_transport_batteries )
"Transported lithium-based batteries are divided into two types: The rechargeable lithium-ion is primarily found in mobile phones and laptops; the non-rechargeable lithium-metal with added restrictions because of its high lithium content is used in sensing devices as well as in some consumer grade AA, AAA and 9V formats. Airlines allow both types as carry-on, either installed in devices or carried as spare packs as long as they don’t exceed the following limitation of lithium or equivalent content:
2 grams per battery for non-rechargeable lithium batteries, also known as lithium-metal.
8 grams per battery for a rechargeable lithium-ion. This amounts to a 100Wh battery.25 grams total per passenger for all Li-ion combined, amounting to 300Wh.
The lithium content of a lithium-metal battery is printed on the label.
Li-ion, on the other hand, uses equivalent lithium content (ELC) that is calculated by multiplying the rated capacity (Ah) times 0.3. For example, a 1Ah cell has 0.3 grams of lithium. A modern 18650 cell with a capacity of 3.3Ah contains about 1 gram. The 8-gram limit permits a 26Ah battery, or 95Wh (Ah multiplied by the Li-ion cell voltage of 3.6V equals Wh). The 18650 is a standardized Li-ion cell of 18mm in diameter and 65mm in length, and is used in laptops, power tools and other devices. Most laptop batteries are in the 60Wh range."
This says an 18650 cell with a capacity of 3.3Ah contains about 1 gram.

I would really like to know the correct answer to this question from someone who knows what their talking about, such as a lithium-ion battery design engineer.