Doesn't that depend on how quickly he corrected himself? If it was in a second interview, and LE spent time pursuing his initial story, would that make a difference? I imagine LE doesn't like going on wild goose chases when 4 people have been brutally murdered. JW (knowingly or unknowingly) was at the center of this crime, in contact with SS (or DW) numerous times Wednesday and Thursday, was at the crime scene (dropping off the money or hanging out) and was privy to SS' normal schedule and habits as his driver/personal assistant. I don't see how providing false information to LE in the early stage of their investigation could NOT be obstructing justice. At the very least, JW wasted LE's time when time was of the essence. If it's true that LE didn't know that SS was one of the dead, LE must have thought he was either in extreme danger or the perpetrator.
Wikipedia:
Generally, obstruction charges are laid when it is discovered that a person questioned in an investigation, other than a suspect, has lied to the investigating officers.... If the person tried to protect a suspect (such as by providing a false alibi, even if the suspect is in fact innocent) or to hide from investigation of their own activities (such as to hide their involvement in another crime), this may leave them liable to prosecution. Obstruction charges can also be laid if a person alters, destroys, or conceals physical evidence, even if he was under no compulsion at any time to produce such evidence. Often, no actual investigation or substantiated suspicion of a specific incident need exist to support a charge of obstruction of justice. https://en.wikipedia.org/wiki/Obstruction_of_justice
HOWEVER, if I read this correctly, in DC in order for it to be obstruction of justice, the lie would have had to take place during an "official proceeding" and a police investigation (on the crime scene within minutes of the crime) is not that. I don't know if interviewing a non-suspect is the same - I guess that's what the prosecutor would have to argue before a judge. It would have to be worth it to everyone (LE, prosecutor, etc) to charge JW and frankly, I think they have bigger fish to fry. It's too bad, because I really think there should be consequences to lying to LE, wasting their time and impeding an investigation. Maybe releasing SWs for his car and phone was a consequence of lying to LE. I believe they issued a SW for NG's phone, and we haven't seen that - I'm assuming because either she's not a suspect OR it's still under seal.
http://koehlerlaw.net/2012/08/wynn-v-us-further-clarification-of-obstruction-of-justice-in-d-c/
ETA: If the case goes federal, that changes everything. Federal obstruction of justice is defined less narrowly.