What on earth were they doing?

 Following negotiations, on November 12, 2002, the parties entered into a settlement and release agreement (release agreement) …

On November 8, 2004, [ESI] filed a praecipe for Writ of Summons. [ESI] thereafter filed a five count complaint on April 7, 2005. In their complaint, [ESI] asserted that the release agreement was invalid because [LSI] induced them to sign it by means of fraudulent misrepresentations. On May 1, 2006, by the consent of [ESI], the trial court issued an order discontinuing counts III, IV and V of their complaint. Accordingly, only counts I and II of [ESI’s] complaint proceeded to resolution on summary judgment. …

On August 7, 2006, the trial court granted LSI’s motion for summary judgment and this Court affirmed that decision on October 1, 2007. …

On October 18, 2006, counsel for ESI sent a letter to the American Arbitration Association (AAA), indicating that the CA entered into by the parties and two amendments to the CA provide for arbitration and that having received no response to its September 12, 2006 letter to counsel for LSI, ESI was "now request[ing] that the American Arbitration Association initiate the process through which an arbitrator will be appointed for the claim initiated by [ESI]." …

By letter, dated October 30, 2006, ESI’s counsel informed the AAA that its October 18th letter was not a formal demand for arbitration, but rather was a request for advice "as to how to proceed" and that if a case number had been assigned it should be voided. Thereafter, the AAA closed the matter, but on November 21, 2006, ESI again corresponded with the AAA and formally demanded that arbitration be initiated against LSI. 

LSI responded to ESI’s November 21, 2006 letter, again asserting that the claim ESI was attempting to submit to arbitration was the same as the claim that ESI agreed to withdraw with prejudice during the pre-trial conciliation before Judge Scanlon and as memorialized by the May 1, 2006 court order. …

Receiving no response to its December 1, 2006 letter, LSI filed a complaint on December 14, 2006, seeking "a declaratory judgment that [ESI] cannot re-litigate in arbitration a claim that was previously dismissed with prejudice…."

LSI Title Agency, Inc. v. Evaluation Servs., 2008 PA Super 126.

Big surprise: ESI lost. They can’t arbitrate the same claims they permitted to be dismissed "with prejudice." (As an aside: they tried to get a new claim in by saying they were arbitrating "breach of the duty of good faith and fair dealing," which, the court reminded, is not an independent claim outside of breach of contract.)

It’s simple: arbitration is not a parallel universe, where collateral litigation is but a passing fancy. If you submit your claim to one or the other, then that’s that (like here). There are limited ways to preserve the options initially, but, once you go through the gauntlet, they’re not going to let you try it again on the other side.