I don’t know how, where, or when it came about, but there’s the idea out there that embassies are somehow “foreign soil”. According to some folks, the American embassy in Japan sits on what amounts to American soil; likewise, the Japanese embassy in Washington sits on Japanese soil.
Allow me to clear this up for you: embassies are not, nor have they ever been, considered “foreign soil”.
I suppose the idea began because ambassadors and other high-ranking diplomats do enjoy something called “diplomatic immunity”. Basically, this means that ambassadors are, in most cases, free from prosecution in host countries. The reason for this is obvious: to allow free communication between government representatives during times of crisis. Diplomacy wouldn’t get very far if ambassadors could be arrested by unfriendly host countries, and if, say, Iran arrested a British ambassador, they might find their own ambassadors arrested in other countries as a form of retaliation. Thus, the Vienna Convention on Diplomatic Relations basically says “don’t arrest my guy, and we won’t arrest your guy”.
This doesn’t mean, however, that ambassadors could go around robbing liquor stores with impunity. Most ambassadors are mature, responsible people who wouldn’t do something like that in the first place. But, more to the point, the ambassador’s home government can revoke his or her diplomatic status at any time, thus rendering him liable for prosecution in the guest country. This rarely happens, however. If an ambassador committed a serious crime, it’s more likely that he or she would be expelled from the host country and would face prosecution at home. Thus, if the French ambassador was suspected of killing a hooker, he would be kicked out of the United States, provided he faced prosecution for his crime back in France.
Of course, diplomatic immunity wouldn’t mean much if an ambassador was considered safe in his person but not his home and papers, so such “immunity” was extended to the embassy grounds itself. And so, in most cases, local law enforcement is not allowed to enter the grounds of an embassy without the permission of the ambassador. This last part is key: if a couple of garden-variety car thieves, being chased by police, ditched their stolen car and jumped over the fence of an embassy, chances good are that the ambassador would, in fact, allow local law enforcement to come in and take the thieves away. At the very least, he would have his own security detail restrain the thieves and hand them over to local law enforcement waiting at the gate.
Note that even this itself isn’t absolute. If the FBI were chasing Osama Bin Laden through the streets of Washington, DC and he jumped the fence into, say, the Chilean embassy, the FBI (under orders of the president) could, in fact, enter the embassy to take him into custody. The Chilean government (and many others) might get extremely ticked off at the US for it, but a couple of phone calls from the President and a few aid checks might smooth things over. This would be something done only under extraordinary circumstances, however.