I just tried an experiment and you're right, WAL mode worked fine across two Docker containers running on the same (macOS) host: https://github.com/simonw/research/tree/main/sqlite-wal-dock...
Could the two containers in the OP have been running on separate filesystems, perhaps?
I dug into this limitation a bit around a year ago on AWS, using a sqlite db stored on an EFS volume (I think it was EFS -- relying on memory here) and lambda clients.
Although my tests were slamming the db with reads and write I didn't induce a bad read or write using WAL.
But I wouldn't use experimental results to override what the sqlite people are saying. I (and you) probably just didn't happen to hit the right access pattern.
"the sqlite people" don't say anything that contradicts this
Perhaps they're using NFS or something - which would give them issues regardless of container boundaries.