I thought the same as you - I only found that link late this afternoon by complete chance.
I tell you what, I got them jumping at DWP and the pensions bit (got 'cut-off' twice and told by the guy at the pensions place that they only did 'pensions' until I said the DWP said they had an ESA section - oh, yes, they have! Sudden recall!)
They are supposed to be calling me back - of course they will (not)
Took me ages to find this link!
https://www.gov.uk/living-in-france
(Scroll down to Benefits in France)
Now whether they are going to come under the 'temporarily' living out of the UK criteria, I don't know. But I do know I caused a certain amount of kerfuffle this evening. I did, however, tell them I was here permanently.
Anyhow, an interesting issue.
This is one link to an old DM article about it - if you read in between the lines you can see it mentions claiming after you move abroad.
The DWPs however are not too keen to discuss the matter.
Is this one of the issues where Europe are saying the UK are trying to opt out and place their own guidelines?
Well, actually I'm not quite sure - I've never claimed benefits and I didn't know what they were when I was in the UK!!! I get lost after jobseekers.
But I'm looking at incapacity/sickness/ESA or whatever the heck they are called now.
I've just discovered that you can claim for some if you have temporary residence, others if you have permanent residence - and I just wondered if anyone had any experience of doing it?
Different rules apply to different benefits, you need to elaborate.