I thought they meant duplicate activities on the Apple Health side. If they can't read what the other services are writing to Apple Health then they have no way of avoiding duplicates.
Doesn't that suggest that Apple is failing to detect and coalesce duplicates, like Strava and (AFAIK) other similar services like Garmin Connect or old MapMyRun do? That seems pretty damning, and also not Strava's problem.
It might be substantially easier to detect duplicates coming from the same device (ie. the Strava case) than duplicates that might have been repackaged by any number of N third parties (ie. the Apple case).