I know that now, it is nearly impossible to join the US Military with any sort of criminal record. I've seen several movies and read several books where either the main character or a supporting character committed some sort of major crime, and was given the choice by the sentencing judge of "jail or military service". How did this work? Were military standards just less strict in the past than they are now, or was this actually an official arrangement or program between the courts and the military? If this was an officially sanctioned program, why isn't it used anymore?
This is an extremely difficult question to properly source, as it is so often difficult to prove a negative and unofficial agreements tend to be...well...unofficial so they don't leave paper trails. There ARE, however, some parts of the question we can answer without the mods here getting too bent out of shape, I hope.
In many ways you have answered your own question. Yes, in times past (let's focus on the Vietnam era, shall we?) US military standards were less strict. Warm bodies were needed, and if a man was physically fit to serve not to many questions were asked. This is an era that sparked ideas like "Project 100,000" that lowered entrance standards to allow more people to be eligible to join.
I'll link to the dread Wikipedia here as Project 100,000 is a well documented government programme which is only tangentially related to the original question.
Colonel David Hackworth talks very briefly in his biography "About Face" about selecting men for what would eventually become Tiger Force and how men who had joined the army to avoid jail were scouted as they may have desirable traits. This is the only "source" that directly comes to mind, as vague as it may be.
Part of the problem with providing records for this is that there simply aren't any. It was an option "supposedly" given to men by some judges, not a sentence handed down by the court. As recently as 2006 a judge tried offering this "deal", but the modern military isn't desperate for bodies like it was 40 years ago.
In the above linked article Eugene Fidell, then-"president of the National Institute of Military Justice and a military law expert." is quoted as saying "There were cases in the ’70s in which GIs tried to avoid punishment under the UCMJ (Uniform Code of Military Justice) by claiming they were not really in the military, having enlisted as a result of facing a jail-or-military choice". Considering the source it seems, at least to me, to be a reliable source of information.
I hope this helps answer your question somewhat, without being too anecdotal.