[TIGHazard]

Why, in this day and age, is it acceptable for an employer to "investigate" rumours of a consensual relationship between employees?

Because there's uncertainty around the circumstances in which they met (it has been suggested that the young lad was around 15 at the time) which of course begs the question of whether Schofield was genuinely helping him break into television, or whether there was an ulterior motive and had groomed him with the intention of having a relationship, once he became of age. Regardless, it was clearly inappropriate for a married man who was decades older to be having a relationship with someone who was young enough to be his son.

There's also additional rumours that would be potentially libellous if they were posted here (so I'm not), but having seen them elsewhere I can understand why ITV investigated. Even if they are 100% fake if someone came to me with them, to not even attempt an investigation would be negligence.