I know that interior linemen cannot go more than 5 yards from scrimmage until the ball has crossed that line. But what happens if a pass is tipped by a defender and comes down within that 5 yard zone? Is an interior lineman allowed to catch it? Can he kill it? Or is he still not allowed to touch it?
In that case, every offensive player becomes eligible.
For that matter, in the NFL, a quarterback who starts a play under center is considered to be an ineligible receiver for that play. (If he starts the play in shotgun formation, he’s considered an eligible receiver.)
But, like with ineligible linemen, if a pass is tipped, the quarterback then becomes an eligible receiver. This is how Brett Favre’s first completed pass in the NFL was to himself. 
There are a few instances of a tipped pass being caught by the quarterback, and ran in for a touchdown. I can’t think of any right off the top of my head, but I’m sure someone else can.
Marcus Mariota did it a year ago. At the end, you can hear the ref saying he was eligible because he was in the shotgun, but that wasn’t a requirement once the ball was tipped. (Without a tipped ball, a quarterback is ineligible if lined up under center, and eligible if in the shotgun.)
Brad Johnson of the Vikings also did it in 1997.
I’ve always wondered and never gotten a satisfying answer: What even is the point of this rule?
Who gives a shit if O-lineman are way down the field? Can’t you just say “You can’t pass to an o-lineman ever, no matter where he is, unless he declares himself as eligible” and leave it at that?
I’m sure I’m wrong or missing something with my rule, can someone explain what it is?
It’s mostly because making everyone eligible is too big an advantage to the offense. Rushing the passer becomes much harder if every blocker could release and be open for a pass.
This StackExchange thread has some good comments. Also noted in the thread is player safety (preventing large linemen from running downfield at full speed to block before a pass play has developed and defenders are ready for it), and difficulty in sacking the QB if he could just throw the ball at the feet of his offensive line.
The point of that rule, and the one allowing only one forward pass per play, and the one requiring a forward pass to be thrown from behind the line of scrimmage, make the game distinct from rugby.
He’s not questioning the bit about making linemen ineligible. He’s questioning the bit about not letting them go downfield before the ball is thrown. As noted, that’s partly a safety issue (no blocking downfield before the completion).
Defensive parity is also a reason no lineman are allowed downfield before the ball. Defensive backs know that anyone downfield is a potential receiver, and the number of players who can be downfield is limited. If all the lineman could run downfield, the defensive backs would need to keep track of which are eligible and which aren’t. Zone defense would be almost impossible if you had to keep track of everyone’s numbers on every play.
The main reason in my mind is that linemen down field tells the defense “run play”, while linemen staying back signals “pass play”. The emergence of the RPO (run pass option) tries to push the rules as far as possible to allow the QB the option to hand off or pass without signaling the defense their true intention until it happens.
Assuming the original question is mostly answered, I have a new one:
Why is intentional grounding a penalty? If you throw the ball away, it’s giving up down for no progress. It seems particularly odd given that stopping the clock by throwing the ball to the ground is allowed - doesn’t seem like a different thing to me.
Intentional grounding is a get out of jail free card. You’d rarely if ever sack the QB if he could spike the ball anytime the defense was bearing down on him. And the NFL wants exciting plays like a sack. As long as the QB isn’t hurt.
The spike is a specific scenario that the NFL wanted because it makes for exciting finishes. Alternatively the QB would just chuck the ball past the LOS and out of bounds, same result, but takes longer.
It’s not just that it takes longer, it’s riskier. Any pass beyond the LOS is a potential interception.
Grounding is a spot foul. It allows the defense to get the yardage, as well as loss of down, that they would have gotten if they’d completed the sack.
For the record, in the NFL, ineligible receivers cannot go more than one yard downfield, and the limitation is until the pass is thrown (regardless of when it actually crosses the line of scrimmage). [https://operations.nfl.com/the-rules/2018-nfl-rulebook/#rule8]
By the way, does anyone know if there is any official NFL guidance or rule saying that ineligible receivers are OK downfield on a screen pass? I can’t see anything in the rules, but it’s never called on a screen, even though the blockers are often way past the line of scrimmage.
As long as they are actively engaged in blocking someone they are legal. And since the screen pass is usually thrown fairly quickly there’s not a lot of time for them to get downfield, especially if they are pulling or otherwise moving laterally. As soon as the ball leaves the QB’s hands they can move downfield.
In college the rule is 3 yards which might be part of the confusion.
Uh … the mere existence of a forward pass makes it different from rugby without any restrictions.
If I remember correctly, decades ago a forward pass deflected from an offensive player could not be legally caught by another offensive player unless it had also been subsequently touched by a defensive player.