[cowboysauce]

>In general, why do individuals and companies appear (to an outsider) to have so much influence in the USA to 'press charges'?

They don't. Individuals and companies cannot bring charges against someone. They can report a crime (like Comcast did in this case) and then the government can determine if they want to prosecute. Someone saying they want to press charges is just signaling that they are willing to cooperate with the prosecution. Likewise saying that you wont press charges is just signalling that you won't cooperate with the persecution. In either case they don't actually have to listen to you.

>since a large company like Comcast could churn out hundreds of vaguely plausible but socially inconsequential claims of fraud

Filing a false police report is a crime. If Comcast actually testified in court then it would be perjury. They'd also likely be subject to lawsuits from everyone they falsely accused once this was all discovered.