To be accused is to be guilty
"Guilty pleas last year  resolved 97% of all federal cases that the Justice Department prosecuted to a conclusion"
Given the extreme lengths of sentences that can be handed down to individuals who force a court into the inconvenience of giving them a fair trial, many people opt to "cop a plea" (and in the process, perjure themselves by swearing they were guilty when they weren't) and get off with a lesser sentence. In many plea bargains, one of the conditions included is that the individual waives any possibilty that they can appeal whatever sentence the beak hands down.
Add to which, it can take years¹ for a person to even come to trial in the USA - during which time they are either in jail or have to raise enormous amounts of bail (and then abide by whatever restrictions are associated with it) and keep paying your lawyers to defend you. None of which is conducive to earning a living or supporting yourself, waiting for your "day in court" to arrive.
No wonder so many people "vehemently oppose" (and with bugger all support from the UK government, looking after its citizens' rights to a fair trial) leaving this country. Once you're in the clutches of the US judicial system, you're as good as slammed up.
 988 days on average in NY. ref: http://www.thenewyorkworld.com/2012/02/27/the-daily-q-how-long-criminal-cas/