My example is much more likely than the one you just gave. Keep in mind what I said before. A huge amount (I estimate probably over 95%) of arrests go from where handcuffs are placed on straight to jail. The example you are giving is one of those arrests where someone is being questioned at the precinct/station. People aren’t stopped on the street for things that happened miles away. In those situations where you are being questioned in a police station - I will clarify. There are two types of interrogations. Custodial and non-custodial. If you were placed in a police car with handcuffs on and taken somewhere to be questioned, that is a custodial interrogation and you have to be read your miranda rights - DO NOT TALK TO THE POLICE. You’re already going to jail. However, if you are asked to come down to the police station, or “offered a ride” and you aren’t put in handcuffs, that is a non-custodial interrogation. You need to be extremely careful about what you say in those interrogations and you might be lied to. If you are sure of why you are being questioned, know you are innocent, can explain what happened without incriminating yourself in anything, AND you can do that without lying, it will probably benefit you to talk to the police. Witnesses are often treated like suspects at first (because the police really don’t know who did what in the beginning) and if you really are just a witness and you can help the investigation, you will probably be better off telling them what you know even if they are suspicious of you. But if you had ANY involvement, no matter how remote, find a lawyer and don’t talk to the police before that.
Most people don’t have their bike’s serial number written down so they can give it to the police when their bike is stolen. You are right that it would be unlikely for someone to be convicted of possession of stolen property if they put up a defense that the bike they had was a bike sold at walmart and the victim didn’t know their serial number. That won’t meet the beyond a reasonable doubt standard. But you don’t need a serial number to be arrested. You only need probable cause.
Vic: “That’s my bike! I reported it stolen yesterday from my house. I live a block away.”
Cop: [looks up police report and the description of the stolen bike matches the bike on scene but no serial number] “How do you know it’s your bike?”
Vic: “My bike had a rip on the seat just like that.”
Cop: [Observes ripped seat, says to suspect] “Where did you get this bike?”
Suspect: “I don’t want to answer any questions until I speak with an attorney.”
Cop: “You’re under arrest for possession of stolen property.”
The cop really has no choice but to arrest in that scenario. Now if that cop wants to guarantee that conviction, he better find some more evidence (surveillance video, picture of victim’s bike before it was stolen matching the bike they just found, witness, etc.). But arrests are more important to a cop’s stats and resume than convictions, so he might stop the investigation right there and let the court sort it out. Regardless, the suspect has now been arrested and has to hope his lawyer can get him off and hope that the victim doesn’t lie even more in court. It’s not a farfetched scenario.