I think what it means is that if more requests come in than the number of available keep-alive connections, then a new one would still be opened up nonetheless.
Additionally, note the preceding sentence to the one you quote from http://nginx.org/r/keepalive:
The connections parameter sets the maximum number of idle keepalive connections to upstream servers that are preserved in the cache of each worker process. When this number is exceeded, the least recently used connections are closed.
Note the "each worker process" part. I would imagine that if a connection (with a new client request) comes in to a worker process that is already past its number of keepalive connections with a given server, then a new one would still be opened up nonetheless, even if some other worker processes still have some of their keepalive connections with the same upstream server still idle.
If you need more details, it'll probably be worth digging into