The relevant law that the FCC is supposed to be carrying out is more specific than the general term "broadband". Rural areas tend to have slower connections, of course, and the FCC is supposed to measure which areas have usable service and which don't. The law says the FCC is supposed to measure whether areas have an option which:
enable users to originate and receive high-quality voice,
data, graphics, and video telecommunications
Voice: Broadcast AM radio is 25 Khz, which very roughly correlates to 25 Kbps. Copper phone lines (POTS) are 52 Kbps max. So most nay internet connection allows for "high-quality voice", given correct settings in the software.
Data: Faster is always better, but Google or Slashdot will load in 2 seconds on a 4 Mbps connection.
Graphics: Facebook recommends uploading at 1200x600 for "full size" display. Such an image will load full size in 1-2 seconds on a 512 Kbps connection.
Video: Netflix 1080p is 3 Mbps.
So it would seem that the standard the law requires them to use ends up meaning about 3-4 Mbps.
We'd all like faster internet, obviously. Te FCC isn't deciding how fast internet should be. It's deciding how fast is required to "enable high quality voice, data, graphics, and video". 1080p is high-quality video, and that's 3 Mbps.