I think that there is a misconception here, not sure. Floridafan on the right track.
When a player gets drafted, no one has to give them anything, it's just an incentive to sign on the dotted line. The more options, the more talented, the more needed, the more the team wants you, the more they will pay you a bonus, within what they consider reason (not counting the first pick or two of the draft).
MLB makes a suggestion that each year, teams sign players for what was received from that "slot" the year before (rounds 1-10 with a cost of living increase). But in reality any team can do what they want and yes, ALL contracts with addendums (where your bonus is mentioned) most likely has to be approved by MLB. Knowing "slot" helps a player to decide if that might be acceptable, an example being if a player is projected 5-6th round, he should know and understand what those 60 or so picks offer in the way of a bonus. Slot goes from high to low considering being a HS player or college, if the slot the year before was for a HS player, and you are a college junior or senior, it will be less and vice versa. BTW, scouts rarely will indicate to you where you might fall, they used to do that, but if they told you that they thought you would go in the 3rd, and you went in the 15th, you'd be pretty ****ed off. That is why, for early projection picks having an advisor is recommended, most likely that person has enough knowledge to see where you will fall in the draft. I doubt my sons advisor would have wanted to become his agent if he thought he didn't have the ability to get to the highest level. If it's just some guy telling you he can get you more money and is not familiar with how MLB and the draft works, stay far away.
What makes players fall in the draft more than anything else is signability, if you are a 5-6th round projection, and you want 2-3 round money, you aren't going to get it. In retrospect, if you are a 1-2 round projection and you fall to 5th-6th, that would take some negotiating, but if they really want you and you really want to sign it'll happen.
So if you hear someone say they signed for slot, that means they were willing to take what the slot position was suggested without countering. My son signed for slot in 2007 and that suggest slot was his bonus, same thing. He just negotiated what they would pay for him to finish school. He agreed to that pick a few minutes before, and one reason was that he felt the earlier pick would in the long run prove more valuable, rather than waiting as he was slipping. It was a good choice for him (as he was given a choice to say yes or no) and he made it quite clear that he was ready to play at the next level and never made any huge bonus demands to any team, other than where he felt he would like to be drafted. Technically he was considered an easy sign, rather than a tough one out of HS. The object is, if you really want to sign, one should be willing to accept what is offered, if not, don't consider it and take your option. I am a strong beleiver in the more honest you are about seriously going pro, the more they listen. So when you tell a scout I really want to play pro ball and then you ask for a half a million and that is not your worth, well do YOU really want to play proball? What do you think the team thinks of that? They think you won't sign so why should we bother.
Also, after the 10th round, a team can sign a player for whatever they want, especially if some of this early rounds didn't sign. You will often hear about players getting a bonus larger in a later rounds than they would have gotten signing for slot, and that is allowed.
The draft has changed since my son was drafted, the new transfer rules and roster rules has made it more attractive for some players when a team flashes lots of money to get him to sign if he is a top projection. But overall is still is the same.
I have a friend whose son was drafted late 20th round, and he signed for exactly what he wanted (125K). He has had opportunities to play in winter ball, where they make a lot of money. He kept his price low because he really wanted to sign out of HS and he knew that if he worked hard he could make up more money in the game. I don't know if he will ever reach the 40 man roster, but he really made himself attractive out of HS, and he really wanted to play proball. That is sometimes how it works. And someone believed him.
I think that people get angry and disappointed at the draft, but reality is if you really do your homework and understand what you have to do to make yourself attractive for signability, it doesn't have to be all that of a mystery.