was valid reason to open an investigation (still TBD btw), that means continuing it once you know it's almost entirely BS and baseless, and even being "sloppy" with your testimony to justify continuing that investigation, is entirely valid too?

Yes Mr. House, there was valid reason to investigate you for the death of Sithie given your prior death wish, but we'll just withhold your legitimate alibi at the time of death, and continue investigating and smearing you. While the media keeps putting you on screen as a suspected murderer.