I saw that other thread, and you just about got it all right there.
As far as shippers and freight brokers having some idea as to the safety and reliability of carriers, going by the SAFER stats for a carrier usually gives a pretty good idea as to who you are dealing with.
http://safer.fmcsa.dot.gov/These are statistics on every carrier that has authority to haul freight by the FMCSA, and can be searched by MC (Motor Carrier) or USDOT number.
Whenever I deal with a broker or shipper I haven't contracted with previously, one of the first things they ask for is my MC number, and I can hear them keying it in to check our SAFER stat.
If your safety rating falls below whatever parameter is used by the broker or shipper, they will not hire you. Some brokers are very finicky as the shippers they deal with only want their freight on carriers that have the highest ratings, say, the top 5%.
I've never been turned down by a shipper or broker.