This isn't accurate. Most node have 300MB mempool size limit (after transaction is deserialized) and currently unconfirmed transaction already surpass the default limit. If you bother visit https://mempool.space/, currently it purge all transaction with fee rate < 1.08 sat/vB from the mempool.
Well, my only source is my experience. And so far every single tx with 1sat/byte fee has been processed eventually just like I mentioned before. Disclaimer: I don't send/receive Bitcoin every single day so perhaps there are periods of time when it won't work. But I've been lucky so far.