I think Marten probably informed Claire (briefly) what was going on when he called her and told her he couldn't make it. I think JWHouk's right, though, that either Marten called to let Claire know he was back, or Claire called to see if he was back yet.
I get the feeling the conversation was more along the lines of,
CLaire: "That must have been difficult for you."
Marten: "Yeah, it was pretty rough."
Claire "I can come over if you want to talk?"
Or maybe she just decided to come over to comfort him. But he needs that now.
And why would he need it now? A good friend is on the edge, was almost over the edge, in fact. But you'll notice that he never gave Faye a hug to comfort her...
Faye established a no-touchy rule early on in their relationship. The one time we've seen them hug was the flower-pits comic. Maybe in their undies, I don't remember (and I'm not up to an archive trawl). But at this point in time, Marten just doesn't feel comfortable comforting Faye physically. Perhaps simply because of the loss of Angus, he thinks it would feel like a "move" to her.
But after the night he just went through, he needs a hug. I'm not suggesting Claire is any kind of substitute for Faye or anything, far from it. And, as another forumite mentioned, after the day (days?) he's just had in the hospital, I imagine he'll be passing out holding onto Claire in pretty short order.
Which, I think, is more what he needs than anything else from her. Just... comfort.
The comic made me weep a bit, by the way. Not squee, just - just tear up a bunch.
But I get emotional easily these days, so take that as you will.
Warning - while you were typing Arizaphale made the same point, only much more succinctly. You may wish to review your post.
Nah, thanks. I'm good.