This is more politics than anything else. The Governor is trying to cut visible things so people will accept the Tax extensions. The truth is, as the the article says, these parks only cost $33 million. In a state where the top 5 highest paid employees make over $10 million in salary (http://www.sacbee.com/statepay/) keeping those parks open wouldn't cost that much.
Plus we just found we've got $2 billion in tax revenue we didn't expect (http://tinyurl.com/3cv3t4k)
Also, for the record, California has a corporate sponsorship program for parks: http://www.parks.ca.gov/?page_id=25426.