If I may, I will add a little more insight here:
First, Truman is correct that when a PRO starts requesting amounts in the thousands of dollars it is probably due to the fact that the venue previously ignored warnings to buy a license. When this happens, the PRO usually does it's homework, and establishes a history of infringement for which it can seek punitive damages. The cost of buying a license to begin with is much lower (see below).
However, to say that BMI is a "for-profit" organization is incorrect.
I recommend that people read the case of BMI vs. CLAIRE'S BOUTIQUE 949 F.2d 1482 from the United States Court of Appeals, Seventh Circuit (1991). In that case, it was established as fact that BMI is a non-profit performing rights organization.
It is also interesting to note that in the CLAIRE'S case BMI offered to sell the defendant a license "at an annual cost of $240 for the first location and $45- 60 for each additional location" depending on the size of the location and the volume of sales. The defendant refused, and BMI then sued them for 88 counts of copyright infringement.
Another case that is interesting to read is BMI vs. STAR AMUSEMENTS 44 F.3d 485, also a Seventh Circuit case (1995). In that case the Court found that BMI "negotiates" blanket licensesw which grant the operator of a bar, radio station, etc., the right to play any of the thousands of songs in its stable for a fixed fee. The Court noted that BMI distributes 80% of the money received back to the composers.
In the STAR AMUSEMENTS case, BMI had Field Inspectors who showed up and kept track of the number of BMI songs played without a license (14). BMI then sued the defendant for infringment, and the District Court awarded BMI the maximum statutory damages ($10,000 for each of the 14 "infringing performances") totaling $140,000.
It is much cheaper for the defendant to buy a license. Punitive damages are designed to prevent future infringements of the copyright holder's works, and to encourage venues to buy licenses so they can freely use the music in the first place.