Evidence of dev testing

When testers test our systems they provide test evidence that shows that what they have tested has worked.

As a developer my dev testing is usually not so meticulous, we have unit and integration tests and when I do my dev testing it tends to be a general feel that the thing works.

A new tester has suggested to the project dev lead that developers should also provide test evidence of their dev testing and the dev lead has jumped up and said this is a splendid idea. I disagree, it's just more bureaucracy and adds no value. In fact I feel that if I am to provide evidence of my dev testing then it negates the need for a team of QA testers because in providing that evidence I am going to do even more thorough testing.

I've never heard of devs providing evidence of their testing and I can't see the point. When I raised this the response was along the lines of 'if we are following an agile methodology then we must do it properly'.

Am I missing something? I thought agile was partly about getting rid of unnecessary work like this.