I don't really know why people count Amy and Rory as "dying while adventuring the Doctor"
They didn't die as companions, they were separated from the Doctor, lived out their entire lives and died naturally. That is nowhere near as tragic as a sudden and brutal death.
Rory would have counted for that multiple times if he hadn't kept coming back.
As Razmos pointed out, they didn't die, they just got sent back in time. They lived a long and fruitful life without him.
Danny wasn't ever a companion, I don't think. I wouldn't classify him as such. Although I guess you could argue it if I'm going to classify Jack as a companion, too.
(and even then, Jack came back thanks to Rose)
Okay.... this is a really weird thing to claim, because the logical structure here is:
episode starts with Amy and Rory as companions, stuff happens, they die within the span of the episode (or two) as a result of being related to the Doctor (this was a big point in the episodes too, with the Doctor flipping out because he had read the book, thereby sealing their fate), and the Doctor leaves companion-less, but in the pleasant knowledge that they lived a full live regardless of their unintended demise. (this is basically softening the blow as writing technique. You get shit done, create change in the main character, everybody is satisfied by the end. It was a lovely send-off )
So, they died as a result of being companions to the Doctor in the length of those episodes (start: companions; end: no companions. Ergo, they dead). They just didn't show it on-screen because that would be awful and unnecessary. That would be a slasher movie thing to do. Or worse: B-movie.
Continuously bringing Rory back was the running theme of that particular season, as is continuously avoiding Clara's death the one in this one so far. The line at the end of this episode however, suggested that as far as 'the judge of time' is concerned, the flip to permanent has already occurred from his perspective (which is definitely a Moffat line, because Moffat loves creepy Doctor, and I fully agree with that), whereas we were shown the linear version with the previous two.
Because you don't want to repeat the same thing twice as a writer (audience can tell, gets bored, ditches book / movie), or director for that matter (go watch Carpenter's The Thing and see how each 'big' - you will know why- scene is framed differently for effect).
Now, a further perversion or 'avoiding repetition' would be to use the death-rebirth cycle for a different purpose, like I previously speculated. That doesn't have to happen, but there are only so many moves that one can make with story before having to repeat yourself (this was Stargate SG-1's problem: they ran out of moves by S5 and then there five more... kind of like Supernatural actually. With that show it's even something of a meta-gag at this point that even the characters themselves are aware of it, and that was two seasons ago).
Also you don't have to shove a stack of dynamite up a characters ass (while I'm sure Clara's is lovely and all) to demonstrate that the character died (see Centurion, unless they retcon that, in which they will need Super Cosmic Hyper Ultra Extra Alpha Large Plus Dynamite -you might see the problem there). We have already seen her being exterminated by daleks on-screen though, so technically she and Jack are already one and two that we have seen on-screen.
Both using 'on-screen' as a "he dead" rule is really silly, because it's just a choice on the writer's end. If Word Of God says "he dead!", he's fucking dead. Until God changes his mind about that, but thankfully, that's usually a different story and a different God.
Popo!
But seriously, creepy Doctor is best doctor. That transition in Blink on "I have until the rain stops" and then the protagonist sitting on an empty bed: beautiful! From the perspective of mere mortals, the Doctor is easily the single most terrifying being in existence (kind of the point of the Pandoricum), and that is just awesome. Can we talk more about that? Can we? Can we? Can we? *squeals*
I forgot to bring that up in a recent 'favorite fictional astronaut' thread: Vashta Nerada. Come on, that black helmet with just a fucking skull in it: yaaaaay!
( I think I need a break from this, it's getting to me )