You said: »I can think of no structure in English where you would use "is" in a similar manner.«
Well, this is not really an argument, since German and English are not the same language. They are related, but not equal.
But still there is such a structure in Englisch:
John was drinking very much beer. Now John is drunk.
But as said before: This does not prove that the German construction is correct, nor would the absence of such an english construction prove that the German sentence was wrong.
But the German sentence is correct.
The verb »passieren« has tree different meanings:
- Ich reise nach München und passiere gerade Salzburg. (I'm traveling to Munich and am just passing Salzburg.)
- Walter passiert die Tomaten durch ein Sieb. (Walter strains/passes the tomatoes through a strainer.)
- Dieses Ereignis passiert jeden Tag. (This event happens every day.)
Number 1 and 2 can be translated as »to pass«, but also #3 comes from »to pass« in the sense of »passing through a period of time«. (Etymology was not part of your question, so I don't go deeper into that point.)
You can use all three meanings in a tense, that is called »vollendete Gegenwart« in German German or »Vergangenheit« in Austrian German. (This tense is built equally in both variations of German, but is not used in the same manner, but this is not relevant here). The latin name of this tense is »Perfekt«.
Here are the (shortened) sentences from above in German Perfekt:
- Ich habe Salzburg passiert. (I did pass Salzburg.)
- Walter hat die Tomaten passiert. (Walter did strain/pass the tomatoes.)
- Dieses Ereignis ist jeden Tag passiert. (This event did happen every day.)
You can see, that - like in english too - you need an auxiliary verb to build this tense. This is equal in English and German. But not equal is the auxiliary verb itself. As you can see in #3 the German auxiliary verb is a form of »sein« (to be), while in 1 and 2 we have a form of »haben« (to have).
German has tree auxiliary verbs:
Haben, sein und werden
sind die drei Hilfszeitwörter auf Erden
You use »werden« to built the German tenses Futur I and Futur II:
Präsens: Ich esse. Du isst. Er isst.
Futur I: Ich werde essen. Du wirst essen. Er wird essen.
Futur II: Ich werde gegessen haben. Du wirst gegessen haben. Er wird gegessen haben.
And you use the other two auxiliary verbs (haben, sein) to build the Tenses Perfekt and Plusquamperfekt, depending on the main verb:
Präsens: Ich schlafe.
Perfekt: Ich habe geschlafen.
Plusquamperfekt: Ich hatte geschlafen.
Präsens: Ich fahre.
Perfekt: Ich bin gefahren.
Plusquamperfekt: Ich war gefahren.
It's the main verb that dictates which auxiliary verb has to be used. There are verbs that need a form of »sein«, others that need a form of »haben«, and there also is a small group that can be used with both of them, mainly according to regional usage (»sitzen« is one of them: »Ich habe gesessen« in northern parts of German sprachraum, while it is »Ich bin gesessen« in southern parts).
If you have verbs with multiple meanings (like »passieren«), it's good to think of them as distinct verbs. Each of them can have its own auxiliary verb, independent form the other meanings. And this is why passieren needs »haben« in the meanings 1 and 2, but needs »sein« in the meaning 3.