Rather than destroying the "brainteaser" tag, it should just be fixed up.
It's not like the term "brainteaser" doesn't have a solid definition. One definition is "something (as a puzzle) that demands mental effort and acuity for its solution". This is quite different from a lateral thinking puzzle, which requires out-of-the-box thinking. A brainteaser requires you to pay attention to the question itself, usually - they're less about "thinking in unconventional ways" and more about making sure you actually think in the box, and make sure you know what the box actually is.
A simple brainteaser is the exact opposite of a lateral thinking puzzle - the answer is obvious, so long as you're actually paying attention and not trying to think laterally. They often require taking things more literally than normal (like "What word in the English language is always spelled incorrectly?" or "How much dirt is there in a hole that measures two feet by three feet by four feet?"), or disregarding information designed to mislead you ("Johnny’s mother had three children. The first child was named April. The second child was named May. What was the third child’s name?").
It's not so much a matter of length. There are brainteasers that make use of length to help hide the facts. But what sets a brainteaser apart from other similar puzzles is that the answer, once given, is blatantly obvious. A good brainteaser is hard to solve, but once solved, requires no explanation.
In fact, I'd assert the neatest, most natural way to describe a brainteaser is "finding the right clues amongst the wrong ones". But the key is that the right clues are the only ones that actually fit together to make an answer. In the "Johnny's mother" example I gave above (which is a simple brainteaser), the names of the first two children look like they're forming a pattern hinting at the answer... but they're a false clue. Similarly, the measurements in the dirt example are actually irrelevant. Another classic example is this one (from another site).