It isn't ridiculous for police to question a guy who murded his girfriend. And IIRC they weren't stupid, they checked with a lawyer to see if that was a legally a request for a lawyer.
Anything more is presumptive.
A witness saying he did it could be lying. A confession could be to sheild a child or another person or an expression of guilt that a death could have been prevented had they done something different.
Shock has odd effects.
Even police arriving on scene minutes after a shot is heard to find the accused holding a gun with blood splatter on their clothes doesn't mean they did it.
Some time in the near future there'll likely be a murder with a time stamped HiDef video of person shooting the victim .. and it'll turn out to be a state of the art AI "fake" for a class project | upcoming film that was being put together just as a third person shot the victim and clubbed the scapegoat over the head.
And if they did, the mere fact that they contacted an attorney to say "does this person's request for a lawyer constitute a valid legal request for a lawyer?" says they absolutely knew that was precisely what was being requested, and were just playing fuck-fuck games.
Because if they weren't, are you (and they) going to argue with a straight face, "No, it was sincerely believed that he was requesting a canine who was admitted to the bar in the state of Louisiana to provide him counsel" then at best you're being absurdist, and at worst, well...
Apropos of ANY of that, the moment the suspect requests counsel (or requests something that sounds sooooo close to requesting counsel that you need to contact an attorney to verify whether they agree that it was a request for counsel or not) you're supposed to immediately terminate the interview. They did not.