Re: But!
No need to concede on that, if the country is relatively friendly the US will arrange a Couch with the host country covering that its troops can be tried for crimes in that country (basically a listing of what the host country can and cannot try for) reasoning behind this is it shows we trust the host country but does limit what our troops can by tried for:
A la yes you can try our troops for stealing, assault, etc.
No you cannot try our troops for leaning against a religious building on Fridays.
The beauty of this too is that once you have been tried and served your penance for whatever crime you committed in the host country you then get tried and sentenced for whatever you did again but this time by a military court.
But yes, typically militaries do not like local countries prosecuting its soldiers, especially if the soldiers are operating within the guidelines of their orders. Especially since many a country that troops get ordered to spend their time in have courts that are easily corrupted and/or are controlled by the local religious leaders and altering laws quickly to hurt your troops or eat up resources in court would be too easy.