The 125% rule does not apply because, basically, the TE is the "orphan child" of the 125% rule from another trade. If you use a TE, it is actually considered to be part of the first trade. In the Harrington deal, it was the completion of the Peja deal. We have two TE's that basically represent "trades pending" from the JO and Ike deals. This is why the expiration date on a TE is one year from the date of the trade.
In the vast majority of cases, the TE is actually considered of value not for it's ability to allow a team to pick up another player, but for its ability to allow the team to shed salary. For example, the Pacers were able to reduce their payroll this year by $2.7mm in the JO trade, allowing them to stay under the luxury tax.
This is why TE's expire the vast majority of the time, with the team holding them wishing to keep the salary relief for themselves (or the more mundane reason that they are simply too small to be useful, like the Ike exception). For example, Denver received (actually, created) a $10mm TE when they traded Marcus Camby to the Clippers, but their sole purpose for that trade was salary relief. They will almost certainly let that expire, in whole or in part, because the salary relief (and, in this case, tax relief as well) is likely of much more value to them than any player they could add.
The Harrington deal was an exception. An odd confluence of events where the TE was "created" by Morway & the Simons as a way to keep from losing Peja for absolutely nothing. It is the only time that a TE was created with the express purpose of being used to get another player rather than salary relief.
Generally, you should assume that teams will allow TE's to expire.