This rumor might have some legs, stock is up 10% this week.
I've no doubt the story is factually correct, even if it was plainly planted by one of AMD's rivals (not hard to guess which one) who counted on it causing a firestorm because most people reading it don't understand how big corporations work.
But a factually correct story can still be a pile of steaming nonsense. In the basement of the Pentagon there is almost certainly a regularly updated set of plans for an invasion of the UK, just in case such a thing should ever be necessary. Their existence is completely irrelevant but they mean a story headlined 'US planning to invade UK!' would not be incorrect.
No doubt AMD has engaged consultants to report on every possible scenario for turning the company around. And one option they'll consider is a break up - it's their job to explore every avenue and devise plans to make it happen if the CEO chooses to go that way, even if everyone involved knows full well it'll never happen because it would be disastrous for the company. But said rival will know that 99% of people reading the story won't understand how these things work and will only read the words 'AMD' and 'Break up'. Job done. They've caused uncertainty, possibly hurt AMD's sales a little and given management and PR another fire to fight.
The reality is AMD are not going to break up. The reason they bought ATi is even more relevant today than it was then; APUs are the future. The consoles have been a very vivid demonstration of the potential of the concept, even if AMD has not yet managed to fulfil that potential in the main PC/Laptop market. PC APUs haven't succeeded so far because AMD has not had good enough technology - the slow, power-hungry Bulldozer derived cores and DDR3's lack of bandwidth ensure an APU ends up as just a slow CPU with mediocre graphics performance.
But next year the technology should all finally be in place. Imagine an APU with a 2000-shader iGPU, four x64 Zen cores and 1-2GB of HBM2 backed up by dual-channel DDR4, something that would give performance similar to an i5 with a 280X. By the time 16nm hits volume production AMD will have this, or something very similar, ready to go. Such a chip wouldn't just be a great product, it would fundamentally change the market (and not coincidentally be an existential threat that NVidia have no way of countering, short of selling out to Intel - this is why NV is firing all guns right now, they have to knock AMD down within the next year or so otherwise the green team's strategic position becomes very grim indeed).
Of course this depends of the Zen architecture being reasonably competitive with Intel. If it isn't no break up or spin-off will save AMD.
.
