A real man (or woman) with significant accomplishments is not self-congratulatory because significant accomplishments are selfless in nature. Moreover, these kind of people don't even have time to brag because they're constantly working to improve things non-stop.
I actually have to disagree with this sentiment in afterthought (many hours of programming and development later with it sitting in the back of my mind...), because it actually doesn't apply to indie game devs at all. We are actually some of the most selfish people as developers, because we generally make the game that we want to play, not what the community expects or wants. A self-rewarding labor of love is most assuredly not in itself selfless by nature.
In fact, why did Notch make Minecraft in the first place? Because he wanted to be known as an indie dev of reasonable quality. (Not even expecting it to explode into something too big for him to handle, just something modest to get started with, you know?) His dream was to sit down, make something simple that he personally found fun, and then go make something else that was fun. By his own standards, for himself.
The community of Minecraft at the time did not want to hear from anyone other than Notch. In I waltzed, out of nowhere, with a feature-rich alternative server, and what was the response? "Don't post it or I'll ban you for stealing money from Notch." But I kept working on it for a bit anyway. A significant accomplishment, and entirely selfish, because I personally wanted a server that could provide basic services, administrative and otherwise.
We are selfish people.
(And programmers in particular tend to be quite eccentric little puzzle-solvers.)
Time to brag is a different issue entirely. Notch certainly had time to make a miniature rollercoaster out of minecart tracks and show it off before releasing it. Was that strictly "improving things"? No, it was adding things, and then 'bragging' about it to build hype. On his blog, where he had time to write out every thought he had, every feature he was working on, and get plenty of general reactions. On what strict schedule are we that we don't have time to brag? Even Nintendo's Smash Bros. games are built entirely on Sakurai's teases and bragging about every little thing his team does (and every character he licenses) nowadays, and the hypemachine it makes is glorious. Raising public awareness that you exist and are amazing is half the business here.
The only way to be 'too busy' working is to completely turn a blind eye to everything that is said about you in return. So yeah, when I drop off the face of the planet for months/years at a time, it's because I stopped sitting around talking about how great I am and how great everything I'm doing is, and started actually doing it. Everyone works at their own pace, and not every little idea comes to full fruition.