DRESS TO IMPRESS, OR NOT

I never cease to be amazed at the standard of dress of some of the very important people I meet as part of my work. In the past couple of weeks I have met the CEOs of two huge, Stock Exchange-listed companies, both of whom wore unbuttoned shirts and no tie.
Perhaps I am wrong? Perhaps it doesn't matter what you wear as long as you get the job done? However in terms of those all-important first impressions it doesn't do a lot for me.