Since I wrote the orginal quote let me clarify what I meant a bit further.
I see resumes at times that say things like:
Responsible for Facility Maintenance
(Well usually I see more like Responible for Database Administration but I wanted to give an example more in line with your question.)
Ok that says nothing about what you actually did because plenty of people don't actually manage to do the tasks they were responsible for. Or don't do them in much depth. Responsible for creating Quarterly reports doesn't mean you actually did them. I have found in interviewing that people also frequently can't answer questions about what they were "Responsible for" if they described the tasks that way.
If instead you said:
As facility manager, I initiated repair requests, I responded to building security alarms, I created access for new employees, I oversaw the rebuilding of the office space to add new cubicles including putting the work out for bid, evaluating responses and hiring the contractor, designing and implementing a plan to move employees to temporary desks while their area was being rebuilt, ...
Now I have an idea of what tasks you actualy did under Facility Maintenance.
Suppose I was looking for a new person who would need to spend a significant portion of his or her time doing facility management (In many companies it is not a full-time job) because we were planning to move to a new building soon. Am I more interested in the person who is "responsible for" it or the person who detailed the tasks?
As far as the example of Led a team, that is an action not a reponsibility, so I am fine with that. It would be better, of course, to say, Led a team who met or exceeed sales goals every quarter for the last 4 years.
The sales trainer is easy to quatify, you should know how many classes you presented to how many students and on what topics. You should also know what classes you designed the materials for.
Basically what I mean was I want to see what you actually did not what you were responsible for doing. I should see the phrase "responsible for" only on tasks that are at best a minor part of your duties. If I need an IT Support Manager who is going to have collateral duty of Facilty Manager that takes up less than 5% of his time, seeing "reponsible for" is ok for that task, but I would want more detail on the actual IT support experience he has and the management experience.