The US town that outsourced everything

This town apparently has a budget of less than $10M/year (since a $20M lawsuit was more than twice the annual budget). It is paying the LAPD $4M/year for policing, which is apparently "significantly" less than what it used to pay for policing, so that means about half the town's budget went to policing.

The policing is being done by the LA county sheriffs' department, and we also know from the article that the administration of the parks has been contracted out to the next town over. For all the bluster about contracting out to the private sector, the private sector seems to have been unable to do the work of the city, and the work was contracted out to other parts of the public sector, which are the only ones capable of doing.

More importantly, since the town is having LA police do the policing for significantly less than it used to spend on policing, it would seem that LA is significantly subsidising this town.

It's easy to run a town with out a functioning public service, if other towns are going to do the work and provide the money. If the police in your town are so corrupt they get convicted of raping and killing people (as was the case here), then other towns might be willing to run your town for you, but this isn' a model that other towns are going to be able to follow.

Or the contract the local police were working under was so rich that LA's actual costs are significantly less. 

It doesn't follow that they're providing the money, only that they're providing the service and being paid for it.  There is no indication in the article that LA is providing the service at a loss.  Only that the service costs less than they used to pay.  For that matter, LA may well be making a profit on the deal which would help subsidize some of the city's own costs.

And there's no indication that LA is operating out of some sense of altruism - sounds like a simple business deal - you pay us $X and we'll provide the following services.

It likely has less to do with contracts, and more to do with acheiving a critical mass that can create efficiency for the required infrastructure. One administrator might be able to support 40 front line officers, for example, but is still necessary when you only have 4 on staff.