It's tough to say why this particular smog station's smog machine had difficulty conducting the smog inspection. We can only recommend visiting a 2nd smog shop to be certain if an OBD II Data Link Connector fault exists. If you were able to connect at home, more than likely, it should connect and communicate with the smog machine as well.
As far as having to drive your Chevy Suburban for 50-60 miles since clearing the trouble codes; this is correct. While clearing the trouble codes, the scan tool also cleared the Emission Monitors. The emission monitors are internal self tests which the engine control module conducts (while your vehicle is being driven) which ensures all emission systems are a GO. Once the monitors are Ready (complete) the smog test can be performed and assuming emissions are low and no trouble codes exist, pass the smog check.