Microsoft's yield issues is still rumor at this point, never has been confirmed and reports of it died down pretty quickly outside of one NeoGAF thread.
I do think Sony would be able to meet demand though, since they're using more common parts and don't have any weird setups with backwards compatibility hardware or their own CPU designs.
Granted, it is all rumors but a lot of it ties together pretty well from some known stuff and other inside rumors as well.
The yield rumor is making a lot more sense along with the other rumors that MS was caught off guard with the PS4. From all accounts it is appearing that MS wasn't expecting to launch the X1 till next year when they were expecting the PS4 and the PS4 they were expecting ended up being more powerful than they were expecting. Sony was looking at doing 4GB of GDDR5 but close to their announcement in Feb they doubled it. This seems pretty straight forward because the dev kits were all with 4GB and Killzone at the announcement was said to be using just 5GB of the ram at that time.
MS dev kits were sent out late and due to yield problems they didn't even have enough to spare to run their X1 games on actual X1 hardware at E3 and instead used much better PC's. Now yes, it isn't uncommon to see games running on PC's at E3, if you a multi platform dev, Sony confirmed that all their stuff was running on PS4 dev kits.
The amount of X1's that retailers are getting for preorder allotment are anywhere between 2-3 times lower than the PS4 as we have been hearing through the retail chains. Which is probably due to esram yield problems as well. MS is also supposedly not even going to be able to start manufacturing till next month as well since they are scrambling to get everything together due to being caught off guard.
The X1 it self is mighty big, especially in comparison to the PS4. Now there can be multiple reasons behind this and I am sure some of these are factored in like MS doesn't want another RROD fiasco and Sony being a hardware company first would have a more efficient cooling solution. But it also can lend to the esram issue of it running hot as well and they don't want to take any chances. For all intents and purposes, on a hardware level the PS4 and X1 are very similar and one shouldn't have any major heat issues, especially when the PS4 has the power brick built into it and the X1's power brick is external.
Basically it all comes down to, MS got caught with their pants down by Sony. They are roughly 3-6 months (can't remember which) behind where they should be if they were planning to originally launch the X1 this holiday season. It is the reason they delayed their announcement back in Feb or March (don't remember), it is the reason why each one of their people has been caught saying different things that contradict each other as they didn't have all their policies and such nailed down yet, and it is why they dance around so many questions like a politician right now because they don't even really know yet for some stuff 100%.
Take that with a huge grain of salt, I do. But a lot of it does add up and make sense and would explain why things are such a clusterfuck on their end (not even considering the DRM/used game stuff). Either way, some of it is partially true and some is probably partially false, it makes for an interesting read imo.