I'll add my story to the thread. We (four of us) just flew home on AA from Coz on Saturday April 17.
On the 14th we went to the International Hospital for our covid tests. We paid 900 pesos pp. Later that evening we each received an email with a pdf file attached of our results (we were all negative.) The next day we stopped by the hospital and picked up a paper copy of our results.
On the 17th we arrived at the airport and a pair of AA reps stopped us as we were walking toward check in. They asked if we had our covid test results; we showed them our passports and results. They told us "great... did you use the Verifly app?" I told them no, and they said "no problem... please just fill this out". We were handed the "I promise I did my covid test properly" form, filled it out, signed it and gave it back to them. They added it to the stack and said thank you.
The rest of the process was standard airport stuff... checked bags, got our boarding passes, went through security, flew home. Customs and immigration at DFW was a breeze, they didn't ask for anything (except our passports.)