The issue with tapes is not the bandwidth, it is the seek latency, could be around ~2 minutes end to end (with the correct tape already loaded). So tapes are not used as random-access, thus no central index on tape archive. The backup software systems keep their catalogs elsewhere.
When I was a beginner I once accidentally created an Amazon RDS Postgres database backed by tape. I was so flustered by how slow it was until I saw the setting.
GP was likely confused by the different types of hard drives (standard, sc1, st1), and assumed it was tape or was incorrectly told by someone else that it was tape.
If I squint hard enough, the only viable explanation I could come up with is GP said "I created the database using the st1 storage type" and someone responded "st!? As in a UNIX SCSI tape drive[0]?"
It could be tape. But perhaps you’re right that it’s HDDs I guess? I assumed most of their normal storage is hard disk and not SSD. They’ve got a lot.
Edit: I checked. You’re 100% right. Well now my anecdote sucks! :) And now, seven years later, I’m back to start on wondering why it was so brutally slow.
If you provisioned a really small amount of GP2, you can run out of I/O credits pretty quickly and get throttled to baseline performance (and it used to be 7 times the storage provisioned, or some such, and now it's 100 IOPS). That's brutally slow for a working database.
When I was in school, the professor of our operating systems class told us about a virtual memory project implementation that had the swapfile on tape. It worked, but it wasn't anything you'd actually ever use.
Latency is absolutely killer with tapes, but bandwidth is still a major issue. The current generation LTO-9 is only capable of 400MB/s in throughput. That's still slower than a SATA3 drive.
Last time I used tape in earnest was a while back though (2005ish), LTO-2 ruled the roost at a whopping 40MB/s, with LTO-3 just making an appearance. Around the time I left the company they were building out a disk storage array as a backup target, and shifting tape further and further away from the main backup path. Data production and storage needs across the industry had long been growing at a greater rate than tape capacity and performance.