Yep, your understanding is correct. When a device connects to your network, it can indeed be counted multiple times across different network components.
This means that a single device can be counted multiple times if it interacts with different parts of the network infrastructure. This is why the sum of clients from individual components (MR, MS, MX) can exceed the total number of unique clients reported at the site-wide level.
To provide accurate data to your client, you may want to clarify that the site-wide "Clients Per Day" metric represents unique devices, while individual component reports reflect the number of connections or sessions across different parts of the network.
I am not a Cisco Meraki employee. My suggestions are based on documentation of Meraki best practices and day-to-day experience.
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