I'd say this is only partially true. These days labels are not, and I would argue should not be the artists' primary target for income. Touring and new media are things artists have control over to a much larger extent and that's where artists should be focused.
If a good independent label wants to pick you up, like say Bella Union or Merge or Sub Pop (still) or the like then go for it, it might help. Or it might not. For some it's a big deal, but mostly in terms of promotion and profile, better tours. The good labels, like Bella Union, get very involved in that side of it, others not so much. Even then those lucky acts that are on good labels are still primarily touring bands, and downloads and sales and royalties are a small percentage of their income, unless something really breaks on radio, and that my friend is whole other ballgame and extremely rare from the average artists' perspective. Better to hope to get on a TV show or film, raise your profile some and get better tours.
Also, most of the time those higher-profile independent labels came along and were interested because those acts already had something going, some sales, regional numbers or whatnot that made the label relationship more like a partnership.
It helps to go into it from a position of strength, where you know you can walk away. And if you can walk away, you might not even need the Independent label. Mostly you need good management and good promotion to get better tour numbers going, build into a position of strength and really think about what means of income are available to you in an age where access to distribution channels (the primary former attraction of labels) are now available to virtually everyone.