What Tony said is valid. But logically an f2.8 lens is still an f2.8 lens. Which means an mft lens gather the same light as a FF lens at 2.8. Yes there's the crop factor and all but to my understanding, it only applies to the DOF and focal length.
I wouldn't say the manufacturers are lying but can you imagine if an mft lens was stated as 5.6 but it gathers the same light as an 2.8 FF lens? That would be confusing to the masses.
Strictly speaking the manufacturers are not lying. However they are not telling the complete truth either.
I think the problem arises really due to the reduction in sensor size, i.e. you take a photo on a smaller sensor and then enlarge it to the same size as an image taken from a larger sensor.
It might be unintuitive in the digital age since image size is usually rendered in terms of pixels instead of actual physical dimensions (like length x width) like during the days of film.
Therefore perhaps it might be easier to consider the following example. Shooting an image on a piece of "full frame" 36mm x 24mm film, and then trying to shoot the same image (field of view etc) on a piece of APS-C 25.1mm x 16.7mm film (this film size actually existed!) and then enlarging it to 36mm x 24mm. You would notice the same effects Tony has mentioned coming into play due to the mathematics involved in shooting on a smaller film size and then enlarging it.
That's the same as debating the pros and cons of 90 horse powers versus 150 horse powers when fetching your parents for dinner. All what matters to them is a safe as smooth trip.
In photography, many factors are more important, relevant and visible than the philosophy of 'real f/2.8' on different systems.
I don't know why you sound hostile, sir. But I'm just giving a general answer to a topic that has countless of debates. And this is a forum after all. Yes, I do agree that apart from technical stuffs, there are things that make photography an art itself.
I apologised if I sound like a Mr Knows It All. But a man of your calibre and experience is way better than to be telling me to "shove it up all in my ass because I'm a newbie" [emoji52]
Differences just from which angle you see the issue from
(if really want to argue, maybe I can suggest that knowing this, you can know the 'quantity' of lighting, and 'depth of field' considerations for composition ;p )