Great questions.
In saying “accurate information” there is a hidden presumption that not all government information needs to be shared. Forget about whether it’s accurate or not and who decides what’s accurate, just be maximally open
The framers discussed this in a few key ways, which resonate ALL TOO WELL with today:
Anti federalist Brutus 1 suggested that in a large republic, representatives will be too far removed from their constituents. Because citizens cannot personally observe public officials, the people "cannot be acquainted with their characters, know their motives, nor be informed of their proceedings." A lack of information would prevent citizens from holding officials accountable.
Anti federalist Centinel 1 directly warns against the manipulation of information by the wealthy elite, arguing that the public can easily be deceived by "well-born" politicians who mask their pursuit of tyranny behind noble rhetoric.
In Federalist 10 and 51 Madison argued alternatively (looks naive today) that a large, diverse republic makes it harder for corrupt politicians or factions to spread misinformation effectively across the entire nation.
In Federalist 70 Hamilton explicitly defended a single, powerful President because it provides accountability. With a single executive, the public knows exactly who to blame for bad policy or false statements, preventing officials from shifting blame or hiding behind an anonymous committee
But the Sedition Act passed only 10 years after the constitution made it illegal to publish "false, scandalous, and malicious writing" against the government, a restriction it could be argued that the government doesn’t even have in itself
Modern law of relevance include the Smith Mundt Act 1948 which prohibited the government from propagandizing its own people (limited to foreigners). The smith mundt “modernization” amendment crammed into NDAA 2012 did away with this restriction and now we have an explosion of govt-payroll influencers , news anchors, talking points memos etc that aren’t exactly…accurate