No there is'nt.
Honestly, this is a really really tricky rule and even a lot of French people don't know it. It's true that with "être", you conjugate the past participles with the subject. But here it's a fake "être". The sentence means "Nous avons téléphoné à nous", you can't say that in French but that's the idea of the sentence. And there it's not "être" but "avoir".
With "avoir", you never conjugate the past participle with the subject but with the complement if this one is put before the verb and if this one is direct. Here the complement is before the verb (it's the second "nous") but it is not direct because you say "téléphoner à quelqu'un" and not "téléphoner quelqu'un", there is a "à" between the verb and the complement. So, finally you don't conjugate anything in this sentence.
I hope I was clear enough :/
Puopjick, I love your explanation.
This is my understanding, and I believe it harmonizes with what you're saying: 1. Some verbs use avoir as the auxillary for the passe compose. These verbs CAN use etre if they are, in a given situation, reflexively used (se telephoner, se parler, se voir), but this is less usual. They use etre in these situations because all reflexive verbs use etre as the auxillary (see item 3). 2. Some nonreflexive verbs use etre as the auxillary simply as part of their ordinary nature, (vandertramp verbs, for instance, like venir, devenir, rentrer, aller), and it has nothing to do with reflexiveness in these cases. Of course, sometimes these same verbs can be used with avoir, but then they assume different meanings in those less common cases. 3. There are some verbs which are always reflexive (se souvenir, for example), and these verbs (along with any avoir verb used situationally as a reflexive verb) always use etre for the auxillary.
Is this clear and correct? Please point out any error i've made.
I did the same thing. I wrote "Nous nous sommes téléphonés" and was surprised when I got it wrong. I think I sort of understand puopjick's explanation. It might also explain whey I got "Les pompiers sont arrivés après que je leur ai téléphoné" wrong because I put an "s" on the end of that one as well.
The only way I can remember this is the clue of the object being indirect instead of direct, which apparently changes everything. But this is exactly the kind of confusing sentence injected by Duo with no explanation in the tips. It would be helpful to hear from one of the experts, but apparently you never know if they are going to see it here or not. Reflects a major flaw in the program. If you know something will be exceptional & confusing without a plan to explain, don't use the example...especially if it's a rare thing.
Could this sentence be translated as "We called ourselves"? If not, how would you say this in French? I know this would be a very unusual sentence, but one might use it in the case where you were testing to see if your phone worked, so you would use a different phone to call your own phone.