I just read this as there being several parameters for trades. The rule you quoted (which was violated in the $1.5m Ayon for $8.7m Anderson deal), is one. I think the cap rule I quoted is another. I think the TPE rule also would apply if we had one.
Plus, there are vagaries:
http://www.cbafaq.com/salarycap.htm#Q26
So being under the cap does not necessarily mean a team has room to sign free agents. For example, assume the cap is $58 million, and a team has $51.5 million committed to salaries. They also have a Non-Taxpayer Mid-Level exception for $5 million and a trade exception for $5.5 million. Even though their salaries put them $6.5 million under the cap, their exceptions also count toward their team salary, increasing their total to $62 million, or $4 million over the cap. So the team actually has no cap room to sign free agents, and instead must use its exceptions to sign players.
So there are at least two different ways to be under the cap: with exceptions and without.
To me, the Anderson trade means we have no exceptions other than the room exception and vet mins (inalienable). I make sense of the totality of what you have posted and what I have posted is that teams under the cap but within `exceptions' of being over and then use those rules if they want. Once you give up the exceptions, you can't.
In my reading, we are in the latter category, and the Anderson trade is evidence.
Thoughts?
ETA: More from the same Question:
A team's exceptions may be lost entirely, or the team may never receive them to begin with. This happens when their team salary is so low that when the exceptions are added to the team salary, the sum is still below the salary cap. If this happens when the exceptions arise, then the team doesn't get their exceptions at all. If the team salary ever drops below this level during the year, then any unused portions of their exceptions are lost (and do not return if the team salary increases).
For example, assume there is a $58 million salary cap, and during the offseason a team has $50 million committed to salaries, along with a Non-Taxpayer Mid-Level exception for $5 million, a trade exception for $2.5 million, and an unrenounced free agent whose free agent amount is $2 million. Their salaries and exceptions total $59.5 million, or $1.5 million over the cap. What if their free agent signs with another team? The $2 million free agent amount comes off their cap, so their team salary (including their remaining exceptions) drops to $57.5 million. This total is below the cap so the team loses its Non-Taxpayer Mid-Level and trade exceptions.
There is logic behind this. The whole idea behind an "exception" is that it is an exception to the rule which says a team cannot go over the salary cap. In other words, an exception is a mechanism which allows a team to function above the cap. If a team isn't over the cap, then the concept of an exception is moot. Therefore, if a team's team salary ever drops this far, its exceptions go away. A rule of thumb is that a team may have either exceptions or cap room, but it can't have both at the same time. However, a team in this situation does qualify to use the Room Mid-Level exception (see question number 25).