How can two separate people be arrested for the same crime at the same time if the police do not suspect them of working together as co-conspirators.

The police need probable cause for an arrest.  If the police have probable cause (more likely to have happened than not) then they can arrest a person.  Accomplices or co-conspirators can also be arrested for the same crime. To convict, the standard is different and much high level of proof- beyond a reasonable doubt.  If two people are arrested for the same crime, but are not accomplices or co-conspirators, each should have reasonable doubt at their trials (blaming the other person).  However, with a lower level of proof- probable cause, it is possible to arrest two persons for the same charge.  Contact a local attorney to sort out these cases and prepare the defenses.