Going to give you some advise that comes from playing this game all my life. Best I ever scored was an 81, but when I play often I am a consistent ball striker. So take it all with a grain of salt and do your own research. Oh I don't cheat either. : )
First rule of business, there are no shortcuts in this game. So please find you a pro that stresses fundamentals, build a foundation, then work from there.
Now comes the equipment. You can't learn the fundamentals with "improvement" clubs. Most of us start with the dreaded slice, but with practice we learn to swing properly and at some point learn to even draw the ball. Buying a club with 2 degrees of closed face will only work temporarily. If you don't correct a slice with your swing, eventually you will be slicing with that "improvement" 2 degree closed offset club. You don't want to be that guy so don't waste your money on that.
You can find pro line used older sets online for $150 or less in good/playable condition. But honestly I would even suggest picking up a nice 5 & 7 or 8 iron for less than 50 dollars shipped. No joke, that is all you need to learn the fundamentals. Learn to hit those clubs consistenly with a proper swing and then you can think about a full set.
Please, stay away from club fitters. I didn't miss out qualifying for the tour because I picked the wrong clubs, and neither did anyone else. And telling a clubfitter you have $500 to spend is like telling a car salesman how much you can spend monthly on a car.
Do your own research and practice practice practice.
But it's less clean / B&W than the old grounded / not grounded rule.
I don't think it's made up at all. Many others have made similar points. It jibes with people's experiences on the course, and absent wind is the most rational explanation for many of the scenarios that have occurred.
Clearly the rules recognize that footfalls can impact a ball's position and tendency to move under the influence of gravity: http://www.golf.com/instruction/ask-rules-guy-can-you-stomp-your-foot-make-ball-drop-hole.
There's also some investigation of cumulative effects of foot traffic. If multiple footsteps / body weight can form a 'lumpy doughnut' around the hole during a tournament, then an individual's steps and weight are clearly having some (if small) impact.
If you dropped your putter hard right next to the ball I could see your point in the last sentence. I would call that a clearly 'at fault' action by the player.
A heavy footfall or a heavy player next to the ball and a very soft, careful grounding of the putter near the ball (or no grounding) would to my mind put the likely cause on the player's steps and body weight.
I personally don't like a penalty for merely stepping into the ball, unless you are unreasonably cloddish about it or intentionally trying to dislodge the ball.
It's 'deemed' so under the rules.
In non-rules land (the actual world), the situation when the ball is clearly at rest to the naked eye are only differentiated by the location of the ball on the green and the proximity of a ball on the lip to the hole. It's a special exception to the general principle according to the location of the ball. This exception is in accordance with the rules as written, but not necessarily the principles which say 'treat like situation alike' not 'treat like situation alike unless the rules deem them to be different'.