They likely contain a transformer but so does my TV and I still call it a TV not a transformer.
The switched mode power supply does to main things it reduces the voltage and it isolates the output from the input.
The simple transformer also does the same.
But the switched mode power supply also controls the RMS voltage to far closer tolerances than the transformer and to reduce weight and cost of the transformer it contains also increases the frequency.
The whole idea of switched mode is we change the ratio of on time to off time it's called the mark/space ratio. There is a minimum time it can be on for and that in turn means there is also a minimum output.
In theroy the poster is correct as long as it draws 10W it should work so putting a few LED lamps on the same supply should in theroy work.
However since the output of the transforming device is not a sinusoidal output but a series of pulses and the LED lamp has to reduce the current to each LED using electronic components they is a chance that one device will upset the other.
To remove all the spikes easy was is to turn into DC again in theroy fitting a rectifier and a capacitor would mean DC but get a simple 12 volt RMS transformer and rectify and use smoothing capacitor and likely the output would be 16 volt not 12.
So the turning to DC must be done with in the device and the device will control the DC output.
Most people would call this a power supply be it designed to run a computer or a set of LED lights it is really the same device.
However raw LED's have to have the current controlled not the voltage. A simple resistor can control the current or another switched mode supply with in the package containing the LED's to differentiate between voltage regulation and current regulation we call current regulation devices "Drivers".
However it would seem lighting manufacturers are calling all devices that power LED's drivers be they voltage of current regulated.
So instead of using a simple name we have to read the specification on the device. If it says 10 - 60 watt its a switch mode device. If it says 12 volt output it's a power supply. If it says 20 mW output it's a driver.
The manufacturers say it's to make it easy but to my mind we should call a spade a shovel.