It must have caused confusion and allowed some people to attempt journeys that were futile, as they mistakenly thought the disruption wouldn't affect them.
Giving the correct station is, IMO, vital so people can make up their own mind on what to do. While the Hertford Loop is known by most commuters (but arguably NOT Virgin EC and longer distance services), the 'normal' route is usually just referred to as the mainline. So you might say that there are no trains running on the mainline via Welwyn Garden City, or better yet, Alexandra Palace to Stevenage. Then with that info, people can surmise that trains are going via Hertford (as they were, albeit delayed) and to not bother going further up/down the line.
Someone at Knebworth or Welwyn North hears about problems at Stevenage and makes for WGC to pick up slow services (by car, bus, even bike), assuming nothing is coming south from Stevenage but they can get a 313 to Moorgate and change at Finsbury Park if needed.
Thing is, it seems that besides the initial message, GN was giving accurate information and saying it was Hatfield - so anyone that followed #Stevenage may have struggled to get accurate info, or any info. It seems someone realised and changed things accordingly.
All in all, given the problems on Thameslink, the best way for someone at Hatfield to get into London would have been to get a bus to Barnet or Queensbury, or get over to Hertford North (or even Hertford East). But hindsight is a wonderful thing!