In your above example, Alice and Bob could both be innocent because the crimes accused are not binary possibilities (If Alice stole Horses, then Bob is lying. If Bob is Lying, Alice did not steal horses). Rather, it could be possible that Alice is stealing the horses and Bob is lying (but had a very lucky guess) or that Bob is not lying in that he thinks Alice is stealing horses because Alice was framed.
It's important to note that the Accusation that Bob is lying is only actionable if Bob knew he was lying and intended to accuse Alice for other reasons. If Bob sees Horses being stolen by a shadowy figure who he thinks is Alice, it's not a criminal offense to report this to police if it's discovered that Charlie is the real horse thief. It is only if Bob had knowledge that would allow him to know it was definitely not Alice at the time he said it. Without evidence of this fact, Bob is in effect saying "I think Alice stole the horses." which is factually true in that it is Bob's opinion that she committed the action, regardless of whether or not he was factually correct.
In your first example, the fact that one crime requires a proven intent (the defimation) and the other does not (stealing horses). In Alice's case, her guilt or innocence hinges on whether or not she stole horses. The Law does not care about if she did it out of greed or concern for the horses' well being. In Bob's case, his guilt or innocence hinges on whether he was making a good faith or bad faith accusation, not whether or not the accusation was correct.
In your second case, U.S. Jurisprudence holds that it is better that 100 guilty people go free than a single innocent man goes to jail. If the police have identical twins Tweedle-dee and Tweedle-dum as suspects for a crime committed by only one twin, but they cannot show which twin did the actual crime, then for the sake of the good twin, it is better to let the evil twin go free then to incarcerate the good twin for a crime he did not commit. Though even identical twins have distinguishing features (for example, one twin is slightly taller than the other, or one has a mole on his face). Even fingerprints on identical twins are not identical, so if the evil twin didn't hide his fingerprints it should turn up. Additionally, while criminal guilt must remove all doubt that the events happened any other way then what the prosecutor said, issuing of warrants only requires probable cause (you can get a warrant to search both twin's property based off the camera as there is a likely chance you'll find it in one of their possessions. Joint property will set us back to square one, however.). Additionally, in the United States, the danger of a chemical weapon being triggered would be an exigent circumstance that would permit a search and seizure without a warrant to be conducted (exigent circumstances exist where law enforcement enters a privately held property without a warrant because of a time critical need for entry. A Bomb threat or a little old lady crying for help that they can hear on scene are often cited example moments where the need to save lives trumps the property owners right to 4th amendment protections and any evidence of crimes found while going through the plain view search of the property is usually permitted at trial. So if an old lady has fallen and can't get up and cries for help, she can be charged if illicit drugs are clearly visible, even though the cops would not have known but for helping her in her distress). The cops searching for a chemical weapon in one of two twin's residences could rise to this level if we do not know their intent but know they have it. The government agency would likely compensate the good twin for the violation to the tune of repairing the damaged door and other property damaged in their search.