Never true for domestic fares. May be true on international.

There are number of travel rules which must be made clear to all users, travelers, passengers but I find hardly anyone is aware of all the important the travel rules.

I just booked a trip ORD-LGA on 6/29 and then back on 7/9 LGA-BOS-ORD. On 7/2 I have LGA-ORD-STL, 7/5 STL-ORD, 7/7 ORD-LGA. I wasn't even aware of the potential of this being a violation and happened to stumble upon this thread. I booked it this way because the outer tickets are company tickets and the inner one is a personal fare. They've were ticketed this morning and I didn't receive and notification of any violation. Should I just wait and see if AA calls me?

Edit: I looked at both tickets receipts and the endorsements/restriction section on both tickets only has this line:

Endorsements/Restrictions -
NONREF/CHGFEEPLUSFAREDIF/CXL BY FLT TIME NOVALUE NONREF/CHG

Does this mean I am in the clear?

I think you are fine if you do not violate any ToC of all these fare.
Sometimes back to back ticket voilate the term of minimum stay.

The big issue here is corp travel agents: airlines are much more likely to nab an agent who is habitually breaking these rules. I recall back in the 90's when we booked all of our travel through live human travel agents at Carlson-Wagonlit. Whenever we started a long-term assignment, we were given a long list of these rules. It was clear that they took them very seriously.

However, one thing is clear: no airline has any legal right whatsoever to prevent your from entering into contracts with other companies. I did MCI-ORD a lot. In those days, you had to nest UA and AA R/T's inside of each other to achieve desirable fares. (By the time I was doing these trips, they'd often match WN's Chicago fares - but not WN's fare rules.)

In any case, short of UAL and AMR merging, those two companies cannot regulate my business with the other. In fact, I think you'd have pretty good legal standing to nest two alliance partners as long as they are two separate corporate entities. But again, I don't think smalltime abusers get sued or denied boarding: the more likely to get busted would be a habitual abuser or a corporate travel agent.

I never nested two UA or AA tickets - these were business trips and I didn't want to risk my miles or status. I nested AA and TW on occasion but stopped doing it when the news of their merger was public: legally, I didn't know if I was really dealing with one entity or not. I think my TW tickets were still a contract with a separate entity, but not being a lawyer or someone who read the detailed fare rules to see if "Don't nest AMR and TW" was added to the rules, I didn't risk it.

Does the purchase of multiple one-way tickets avoid this problem altogether? I would think that they could not put any stipulation on what you do after your one-way flight lands.

It avoids this problem but creates another one - cost. The reason that people book trips like this is that they are much less expensive in many cases. If it were the same price to just book the one-ways then booking "normal" r/t flights would also be reasonably priced and there would be no need to do it this way.

Not quite...

What about mileage runs? Sometimes you run into this situation when trying to "force" faraway connections. For example, one-way fares through Florida are cheaper and insert longer legs into a cross-country MR.

And there is nothing wrong with those routings/tickets as they are not being used to circumvent fare rules.