Yes, when it comes to anonymizing a source, releasing no information is always better than releasing any information, even if that information is a mix of truths and falsehoods. But, releasing a mix of truths and falsehoods or less specific/more generalized truths can only be equally as bad as releasing all specific truths, but it may turn out to be much better. Saying your tenure was September 2016-August 2017 might match 20 people at the company, one of which is your source. Fudging your tenure to August 2016-September 2017 might match 20 people, but not your source. Saying your tenure was 2016-2017 might match 1000+ people, including your source.
There are trade offs in all of these methods, but I don't see them as being particularly wrong if you want to provide color to your story without materially affecting it, and can be confident that you aren't helping to identify your source.