Well, yes, but ETB also know the difference between País Vasco the official part of Spain, and Euskal Herria the historic Basque lands. Hence why they show Nafarroa, Le Pays-Basque Français and parts of Cantabria and La Rioja on their weather forecasts, but in a slightly different colour to País Vasco itself.
It could be like that problem that they have in Britain with a channel owning some rights but not using them; TVE may still have the rights to the race but no intent to show it, so ETB may have their hands tied anyway; maybe ETB themselves simply do not want to or cannot afford to cover it, having already ploughed resources into showing Euskal Herriko Itzulia (which is screened on ETB1 and yet also available online). I suppose the local following of the sport may merit a highlights package or a brief report, but the international interest isn't enough to merit putting it online via ETB-SAT.
ETB-SAT is broadcasting the Athletic match tomorrow afternoon. I suspect that comes with a bigger audience than the GP Big Mig, sadly.