"Intuition" and "common sense" are nothing more than predjudices. They may be right; after all, prejudices are usually founded in real-life experiences.
The problem comes when you over-generalize those experiences and crystalize that over-generalization as knowledge.
A silly example: you run a test on a website about button colors and red is the best color and that it made a large difference.
There are a lot of lessons you could possible take from this, e.g., 1. Users prefer red buttons over any other color 2. You should always test button color 3. It's important to think about what draws users' eyes and test that, including buttons. 4. It's important to test everything, no matter how small
Learning (1) is probably wrong. Red might work in this situation, but not in another. This is the problem with learning tactics in general. As the competitive landscape evolves or the situation "on the ground" changes specific tactics become less useful, and might even be worse than an alternative you've precluded because of your "expertise."
(2) and (3) are probably good lessons to take away. (3) is better because it opens your eyes to new, possibly fruitful things to test, although (2) isn't bad.
(4) is the opposite of (1) in that it's an overbroad lesson that is hard to apply and if done religiously would probably paralyze the decision-making process.
Anyhow, that's how I think about applying "data-driven" processes to business, marketing, and product decisions.