Yes, you either need to have a per-customer uptime number (that is visible to those customers) or you have one unified uptime number that takes a hit if any customers experience downtime. You can't have it both ways.
Why can't you maintain and report an average uptime across all service usage? So if you have an outage that affects 1% of traffic it moves your figure 1/10th as one on 10% of traffic?
That's what I'd expect a reported number to be, since that's what a client experiences on average.