The New York Times is a for profit company. Does it have no fourth amendment rights?
If the New York Times was involved in a major scandal, and their response was "I plead the 5th", and refused to give any details, well I as a human being absolutely can judge them on their decision to not explain themselves, and I absolutely can judge them guilty.
Don't like it when I judge you guilty and treat you as guilty? Then be more transparent and try and convince me otherwise.
This is quickly becoming older than the stupid "First Amendment only applies to government so it's okay to censor opinions we don't like!" trope. Innocent until proven guilty isn't just some quaint legal principle, it's supposed to be a foundation of American society (and many like it). The legal system is ultimately just a mirror of society; if we disdain such principles for long enough they'll disappear from the courts as well. Many people would be happy to see that happen; perhaps you're one of them, perhaps not.