So the person who says they text their kids from yahoo is actually sending an IM, yes? Which is not handled quite the same way as you CAN reply.
Checked this on yahoo site (Im not using Yahoo Messenger, BTW, just my yahoo mail service):
Text messaging is sending and receiving written messages on a variety of devices via short message service (SMS).
Send a mobile text message to any mobile device. Just click New Text on the left side of your page.
Youll also see your contacts with saved numbers listed under Mobile Contacts on the left side of the page, under Chat & Mobile Text. (Dont see any names or numbers? Just click Mobile Contacts. If youve saved contact information for anyone that includes their mobile number, they should appear here). Click on a name or number under Mobile Contacts to begin a mobile text message.
So... yes it is sending as SMS (short message service), the same as a cell phone sends and receives.