I don't see a problem with placebo patients doing better than...

I don't see a problem with placebo patients doing better than average of other studies. What matters is how much better the treatment groups are compared with placebo. It would be seen as a strength of the study if effectiveness of treatment is amply demonstrated despite the placebo group doing better than expected.

I know that the risk here is that the treatment might not be that much better than placebo. But that risk is inherent with all clinical trials. It would be terrible after all this time to have an effective treatment but where the trial results can be put in doubt by a flawed design implementation -- where the placebo results are made worse than they otherwise might be. That's not the case in this trial: efficacy over standard care is going to be demonstrated without question or not at all. I think the first will apply.