Your question highlights the problem of "Marketing Math" when it deals with networking gear.
Yes, the total backplane throughput of a switch would be the sum of the port speeds. The trickiness arises when you start looking at spec sheets for chassis based switches. You have to consider the bandwidth of the backplane for streams to and from an individual switch blade. In order to ensure that your switch is non-blocking, you need the throughput of the interface for the switch blade to talk to the backplane to be double the port capacity.
Consider a hypothetical 2 slot switch...each slot populated with 2 ports of gigabit ethernet where each port on the switch is sending its data to the same numbered port of the other switch blade:
- Slot1/Port1 -> Slot2/Port1 @ 1Gb/s
- Slot2/Port1 -> Slot1/Port1 @ 1Gb/s
- Slot1/Port2 -> Slot2/Port2 @ 1Gb/s
- Slot2/Port2 -> Slot1/Port2 @ 1Gb/s
Total of 4 Gb/s, just like your example, but consider the bandwidth to and from the backplane for the same traffic pattern from the perspective of Slot 1:
- Slot1/Port1 -> backplane @ 1Gb/s
- backplane -> Slot1/Port1 @ 1Gb/s
- Slot1/Port2 -> backplane @ 1Gb/s
- backplane -> Slot1/Port2 @ 1Gb/s
Total of 4 Gb/s for the 2 port switch blade to talk to the backplane. The same applies to slot 2, so if you're measuring the sum of the bandwidths of the switch blades talking to the backplane, you come up with 8 Gb/s. While the backplane internally only has to be able to handle a total throughput equal to the port capacity, the interfaces between the backplane and the switch blades of a modular chassis will sum up to double the capacity.
This is why reading spec sheets on networking gear is not always a straightforward task and sometimes requires some digging to understand what the actual data the vendor is presenting to you is representing. Some will, for backplane bandwidth, quote the throughput of the backplane itself, while others will give you the sum of the interfaces to the backplane from the switch blades.