I have a different take. Private channels support parties that align with their interests. But private channels will criticize there government non-stop if they do not like the current ruling party. So, it's way more complex that everybody works for the government, that seems to be true in China, thou.
However, when the pandemic started the government spent over 15 million euros directly in private televisions [1], and gave over 100 million euros in institutional advertisements to radio outlets, newspapers and the aforementioned private televisions [2], supposedly to avoid their economic collapse. Also some regions did the same with regional or local outlets.
So, it's not like they're at their service... But why should the media in Spain criticize the hand that feeds them?
[0] Note, sources are in Spanish (and both sources got institutional advertisements!):
[1] https://www.lavanguardia.com/television/20200331/48219498329...
[2] https://www.elespanol.com/invertia/medios/20200407/moncloa-a...