Indeed, Dumbledore and his allies are being somewhat less than maximally clever here… it would make more sense if they simply didn’t know about the other student with a Time Turner because it was an unauthorized copy, or something. (And it’s quite apparent that Time Turners are far more common in the MoR-verse than in canon, Hermione was only able to get one in book 3 was said to be a very unusual event which was only happened because the staff had an extraordinarily high level of trust in her.)
Indeed, Dumbledore and his allies are being somewhat less than maximally clever here… it would make more sense if they simply didn’t know about the other student with a Time Turner because it was an unauthorized copy, or something. (And it’s quite apparent that Time Turners are far more common in the MoR-verse than in canon, Hermione was only able to get one in book 3 was said to be a very unusual event which was only happened because the staff had an extraordinarily high level of trust in her.)