Yup, exactly this. The discount in a tender offer is normal. DST also discounted Facebook back when it made a $100m tender to existing employees and shareholders. Look at how TechCrunch reported on that tender offer when it happened:
Furthermore, SoftBank has a lot of leverage that DST did not. SoftBank has invested in Ola, Grab, Didi, Nvidia, etc. and threatened to invest in Lyft. It has leverage that allows it to get a better offer than what any other investor could get.
https://techcrunch.com/2009/07/13/dst-to-buy-up-to-100-milli...
Furthermore, SoftBank has a lot of leverage that DST did not. SoftBank has invested in Ola, Grab, Didi, Nvidia, etc. and threatened to invest in Lyft. It has leverage that allows it to get a better offer than what any other investor could get.