Two factors are the most significant limitations to download speed: the speed or bandwidth of the communication channel, and the speed at which the remote server can pump bits into the channel.
Broadband has practically eliminated the speed of the channel as a consideration. You still see it sometimes with overseas sites.
That leaves server speed.
Big sites like the New York Times or Washington Post have server farms that are designed to handle millions of hits a day.
Small newspapers may not even operate their own servers. They may use a low-cost web site host or piggyback on another company's site. If one of those servers gets a lot of hits because of a popular story, the server will not be able to keep up with the traffic. It will be bogged down by disk access times and memory limitations, the same as any computer performing an intensive task.
You can test your Internet connection speed
here or at any number of other sites.
(IANAL, but I am an electrical engineer.)
- Jim