What does the Slow attribute of a Connection object precisely mean?

Issue

While investigating how to detect and handle slow consumers, I have detected a discrepancy in JMX.

The Slow attribute at connection level does not match the SlowConsumer attribute at subscription level.

Here is a concrete example with a connection (with Slow=false) that has a single subscription:

org.apache.activemq:brokerName=xx.xx,connectionName=ID_xx.xx-8627-1460620754907-1_655311,connectionViewType=clientId,connector=clientConnectors,connectorName=stomp,type=Broker = {
   "Active" : true,
   "ActiveTransactionCount" : 0,
   "Address" : "xxx.xxx.xx.xx",
   "Blocked" : false,
   "Broker" : "xx@xxx",
   ...
   "Producers" : [],
   "RemoteAddress" : "tcp://xxx.xxx.xxx.xx:xxxxx",
   "Slow" : false,
   "UserName" : null
}

And here is the corresponding subscription (and it has SlowConsumer=true):

org.apache.activemq:brokerName=xx.xx,clientId=ID_xx.xx-8627-1460620754907-1_655311,consumerId=ID_xx.xx-8627-1460620754907-1_655311_-1_1,destinationName=xx.xx,destinationType=Topic,endpoint=Consumer,type=Broker = {
   "Active" : true,
   "Broker" : "xx.xx",
   ...
   "Selector" : null,
   "SessionId" : -1,
   "SlowConsumer" : true,
   "SubcriptionId" : 1,
   "SubcriptionName" : null,
   "SubscriptionId" : 1,
   "SubscriptionName" : null,
   "Type" : "Topic",
   "UserName" : null
}

So, why isn't the connection marked as being slow? What does the "Slow" attribute on a connection object precisely mean?