You're arguing about the wrong thing: I still think the parent's position is reasonable and that's it's fine to only care about performance up to a certain percentile.
Maybe you don't like 99% and think it should be 99.99999%. Fine, doesn't matter. Do what makes you happy for your web app.
And besides, this "measurement" has nothing to do with the functional reliability of the app. 99.99% of requests completing within 100ms doesn't mean the other 0.01% of requests fail (as another poster noted); it just means they take longer. If you're worried about requests failing (as we all should be!), then that's a separate issue to deal with. So then you say something like, "99.99% of all requests must complete within 100ms, and no more than 0.0000001% of requests are allowed to fail on average." Or something like that.
Maybe you don't like 99% and think it should be 99.99999%. Fine, doesn't matter. Do what makes you happy for your web app.
And besides, this "measurement" has nothing to do with the functional reliability of the app. 99.99% of requests completing within 100ms doesn't mean the other 0.01% of requests fail (as another poster noted); it just means they take longer. If you're worried about requests failing (as we all should be!), then that's a separate issue to deal with. So then you say something like, "99.99% of all requests must complete within 100ms, and no more than 0.0000001% of requests are allowed to fail on average." Or something like that.