While I can see their point I don't think it's a strong one. And I suspect very few people subscribe to it. Frankly, I think saying thanks is very important. Firstly, you are showing appreciation. It's just good manners, which are very important online, just as they are in the real world.
Also, you are helping the person who retweeted or mentioned you build his following to some degree. People will see his handle, and a certain percentage of your followers are sure to click on it. Some will follow in time. Of course, the more people who follow you, the greater this effect.
And by saying thanks you're also establishing rapport and trust -- even just a little bit. You may not decide to build on this later, but it's still a sensible thing to do.
You're also making yourself a bit more appealing to prospective followers who are searching the site. When people who are looking for others to follow see a few @replies showing gratitude to others they know that you may well thank them if they follow and retweet you. (Of course I can't prove this; it's just a hunch. But I suspect that it does increase the likelihood of someone following you just a little bit.)