The US cannot force those companies to lie. They can force them to stay silent, in which case they'd just say "No comments". If those companies are lying, they are committing security fraud.
When it comes to companies like ATT/Verizon it seems like no forcing is necessary. They are complicit.
But they can. Maybe only in cases where silence is a canary, but that still sets a precedence for them being able to force you to lie.
Would the US government have to force these companies to lie? It's quite possible that the denials were the result of voluntary cooperation.
A company has to follow court orders. The government would have to sue itself.
Now, a court order would indeed be something different, but I find it hard to conceive of a judge compelling a company to lie.
That's a nice government tender you're working on, looks very profitable! Would be a shame if someone rejected it because reasons.
While it isn't the direct influence described i imagine this scenario is highly effective and getting companies to stay in line.
The companies may have a strong incentive to cooperate in this campaign too, both to save face and government relations.
Unfortunately all of Bloomberg's allegations don't hold much water either, even though it'd be so easy for them to make the story credible with some details.