The details of trial/evidential procedure matter here.
The Met say he was identified as Dr T. But that would have to be established in Court. The say so of the Met is not conclusive.
The reason it can work for the defence, is that they can easily call PJ witnesses and public records to establish "tannerman" as the prime suspect. They can presumably call PJ witnesses who were there when JT was asked to identify RM. This raises an evidential plank that an alternate prime suspect existed.
Evidential burden would then fall on the prosecution to show it is not a reasonable possibility. Having to call Dr T, Met detectives, JT etc to prove that "Tannerman" was ruled out is likely problematic.
IMO HCW won't want to go down that route at all. He will want to say Tannerman remains a mystery, but we don't need to delve into that night at all, because he has other evidence that so strongly connects CB to murder, that it must be him and we don't need to get into the whole Tapas timeline
my 02c