> if ground stations are the bottleneck

You’re half way right and I think this is why Iridium is claiming speed - they’re reusing marketing material without specifying which conditions hold true.

Ground stations are the bottleneck in two situations:

• example: customer is in Australia tracking a product on other side of planet. It needs to somehow get the data back to Australia.
• example: a user wants to send an emergency message to another user, like using Garmin SOS device.

But with emergency SOS the ground station nearest you will be the one handling your request, so beaming across multiple satellites is pointless.

Also iridium has less total number of ground stations, so less coverage on earth, they just make up for it with better satellite-to-satellite coverage