Sanders and Lieberman were the I's that caucused with D's.

Franken sworn in July 9, giving D's 60 for a month and a half until Kenedy's death Aug 25.
Kirk (Kennedy's appointed replacement) was sworn in Sept 25, giving D's 60 again for 4.5 months until Brown sworn in Feb 4.

You could argue that Kennedy's 1.5 months didn't count for much, but the 4.5 months still counts.  And again, knowing Kennedy's replacement would be there in a month, it's easy just to delay votes for a month since D's controlled the timing.  

The Gang of 8 was 4 years later, well after D's had full control to do whatever they wanted (like they used to pass Obamacare).