[wolrah]

Correct. I can say for sure that Gmail does not reject for missing SPF records, I send voicemail-to-email messages from VoIP systems with no DNS records all the time.

Gmail will accept anything that isn't actively failing anything, even spoofed nonexistant domains, but it will likely get flagged as spam.

If the host is the (or one of the) A/AAAA records for the From domain it'll generally not flag as spam.

If the host is not, then SPF records are required to be reasonably confident it won't get flagged.

Office 365 is a bit pickier and Yahoo is a pain in the butt. Fortunately I deal with mostly business systems so telling the end user "stop using Yahoo for your company voicemails" is reasonable.