It's a no-win situation. If there was separation, that goes against the claim that they were living together for the 3 years. If there was no separation, it means both were living outside the US. Either way leads to denial.
I disagree. The main problem was that she claimed that the husband had permanent residence overseas. That was the key to denial. Because if she resides overseas, she abandones GC. But if she resides in the US, that means separation from the husnband.
If he resided permanently in the US, but stayed temporarily outside, the situation is very much different. Then they both resided permanently in the US and together. No problems with residence, no problems with separation.
It does not follow that a naturalization denial for breaking continuous residence would also result in revocation of the green card for abandoning residence, because the criteria are different. For naturalization it is more strict; for example if you go away for 2 years with a reentry permit, your green card will usually be preserved, but you usually would be considered to have broken residence for naturalization purposes.
I do not think they are more strict. They are more or less similar, but a little different. For keeping GC what does matter is intent to live in the US permanently. You could go abroad, but with an intention to keep residence in the US. There are limitations - one year without RP or 2 years with RP mean abandoning GC, unless a returning resident visa is obtained.
For continous residence it is less intent, but more actual dwelling place.
So, if you leave for Canada just for 1 day to establish permanent residency there (get a Canadian PR status), and then return back to US (without changing the place of your dwelling), you keep continuos residence in the US, but abandon you GC.
If, instead, you go to England for 1.5 years with a reentry permit to study, you keep GC, but loose continuous residence.
here in order to figure out why Gc was ot abandoned, we need more information. I would say, the dates of employment in the US and abroad. The dates of all entries to the US and abroad. I am pretty sure the requirements are actually very similar in terms of real life situations (not hypothetical examples).