LT, I think you didn't understand my post.
Of course if a German murdered someone in another country and the evidence of it would be supplied to German authorities, then that person would be tried for murder in Germany.
In fact, no matter where you are as a German, if you do something that's a crime under German law and you get back to Germany, you will be tried if it comes out, because simply for being a German, German law applies to you IN ADDITION to whatever foreign law the other state has. So, for example if a German commits in a murder in a country where murder would be legal (ok, very hypothetical), he'd still be committing a crime as far as German law is concerned. I remember some cases of child molesters who abused children in Thailand. The were never tried there (even tho that's a crime there, bribery obviously makes authorities look the other way there). But, as evidence made its way to Germany, German DA offices were very happy to build cases against them.
The reason Germany (and afaik most other countries) have laws in effect that prevent extradition of their own people to the jurisdiction of other countries is, in fact, a very simple one: Sovereignity and security.
Imagine: Some country named Weirdland would make chewing bubblegum a crime punishable by death penalty. Some of your countrymen chew bubblegum there on their vacation. Then they fly home. A week later Weirdland's authorities demand extradition of your countrymen so they can be tried in Weirdland, possibly facing death penalty. I don't think you'd be very happy about that.
No-extradition laws for one's own countrymen prevents them from being tried for "crimes" or with penalties that are unknown or unacceptable in their own country.
It's also a way to prevent other countries from building ridiculous cases against another country's people. Something that used to be very "popular" until the end of the cold war. For example, imagine a CIA agent doing some stuff in the Soviet Union (nothing illegal, just gathering intel). His activities are discovered by Soviet counterintel only after he returned home. Now Soviet authorities build a case against him and demand extradition. Would you really want the USA to hand the guy over to some Soviet judge (who, of course would be totally neutral)? I think not.
As a side note:
To make matters (in Europe) more complicated, there is within the EU a European arrest warrant. The regulations about it also state that if someone is arrested in one EU country for committing a crime in another EU country, he has to be handed over to that country for trial. So far, there is no clear judgment on how that is to be interpreted if the person is German on and found on German soil. Technically in such a case extradition would be a violation of the German constitution. So the question is what's on top: the EU treaty or the German constitution. There's no case requiring clarification yet, but if there ever is, it will certainly make its way into law history. (And depending on its profile may cause a big problem for the govt).
Addendum:
There is also a UN treaty that defines certain crimes as crimes acknowledged by all UN members. Naturally all the capital crimes like murder, rape, armed robbery, crimes against humanity etc. So no matter where those are committed, the home coutnry would have to investigate and try these if there's probably cause. It's one of the reasons Interpol exists.
Of course, it's theoretical and heavily influenced politically when it comes to war crimes (which have little to do with justica but more with in whose favor a war ended).