Not a problem. We flew SAS "economy class" Feb 2016 SFO-CPH, then CPH-HEL before returning HEL-CPH-SFO. We had one checked bag per person plus one carry-on in the overhead and one personal bag each without any extra charge.
I believe that your confusion may come from the SAS web site that shows some kind of "go light" super economy fare that limits free baggage: http://www.sasgroup.net/en/sas-go-light-for-those-who-travel-light/
On 8 September , SAS will be introducing a new concept – SAS Go
Light. This new offering is a supplement to the existing SAS Go and
SAS Plus, and will be available on routes between Scandinavia and
Europe. SAS Go Light is aimed at customers who want to travel only
carrying hand luggage and secure their seats at the lowest possible
price, and gives SAS’ customers an even greater choice to satisfy
their travel needs.