If you don't learn everything, then you must have some independent criterion with which to pick and choose; and having such a facility, one may as well simply start down whichever path one feels is most appropriate anyway.
In other words, if you can somehow rule out large swaths of possibilities without even trying them, then you must have some intuitive feel for the problem (or at least, have an intuitive feel for what you think the solution is likely to resemble, whether or not you turn out to be correct). In such a case, you are investigating based on your own intimations and your efforts will develop from there, rather than from from a top-down view -- which has so far been amply demonstrated not to work.
Edit: The recommendation to look "everywhere" is untenable, because at some point you have to stop casting about if you are going to get anything done yourself.