Hyph,
You are quite right in what you say, but there is a bit of a wrinkle in that ICMP traffic (including ping) is usually given a lower (if not lowest) priority by ISPs and peering carriers, and is sometimes delayed or dropped entirely on busy links.
So delayed ping can indicate congestion on a link, which can also show as reduced throughput or download speed. The congestion can be caused by high traffic volumes or a fault.
If the ping response time from the same target has increased, then either the route distance has increased (which may occur if it has to route around a failed path), or there is congestion. Or both.
SD