Quite simply, the answer here is that while one can retrieve emails from a POP box when connected via another ISP, one cannot transmit emails via an SMTP server when connected via another ISP.
As noted above, this is to prevent spammers.
What is needed is access to an authenticating SMTP server. Such a server needs a login (login+password). (When you send emails via your own ISP's SMTP server you don't normally need a login for that because it authenticates on your IP.)
Lots of commercial outfits offer these servers, for some money.
Or, if your company runs its own POP server, it could just as easily set up an authenticating SMTP server.
With a strong password, and correctly configured, it should be safe.