Uncontended is not about the bit from your lair to the PoP, its abut the bit that goes from the exchange/PoP to "that internet". Basically, to use home DSL as an example, everyones line will run as fast as it is able, eg 8Meg on DSLmax. but if your ISP sells 50 8meg dsl lines in your area, they will probably only have a 10Mb link to the internet, hoping not everyone's on at once. This is the way it works in LAs generally. If you are paying for uncontended - and you'll pay more, sometimes a lot more, but you should get the advertised rate whatever the weather :)
This in essence is correct but could be expanded slightly. There are two points of contention.
The first is the point from your local exchange to the ISPs backbone and then from the ISPs backbone to the Internet.
The ISP incurs most of it's cost getting the traffic from your exchange to their backbone. The bit out on to the internet is cheap.
If you stick with the broadband example then the cost to get the traffic from the backbone to the Internet is less than 1% of the cost of getting it from your exchange to the backbone.
Most contention on broadband comes from ISPs controlling the bandwidth used from the exchange to the backbone to keep costs predictable.
Leased lines come with zero contention and although carried in the same way have guaranteed bandwidth.
Not sure if that helps a little more.