One way tickets

When I suffered a burst appendix my ex husband flew down to help me after the surgery to save my life. They refused to sell him a one way ticket even though he explained he didn't know when I would be well enough for him to return. He had to purchase the return ticket and we were forced to extend the date for another fee when I needed him longer than expected. There was no explanation and in his luggage was medical supplies urgently needed for my recovery. It took another surgery and his return again, but I'm still here and as strong as ever.

I don't remember what airline he was flying, but I know how upset he was when he arrived. This was 6 years ago and he bought the ticket online, but was forced to buy the return at the ticket counter when he checked in. There was no time to argue as he was already at the airport. I woke up ill on Dec. 5th and wasn't diagnosed and operated on until Dec. 22. I nearly died and the Dr. didn't give us much hope for my survival. I was kept awake for the three hour surgery to remove the rotted intestine sections, piece them together and fit me with a colostomy bag while they healed. A month later I was dying again from the two months without nutrition and the decision was made to hook me back up even though my kidneys weren't working.
Four days later they started back up and I left the hospital.

Have flown down to Mexico numerous times one-way from the U.S. and have never had a problem. That said, it's best to heed the advice Lunateak kindly shared and be prepared.

Frommer's and CNN recently published really good articles on which airfare search engines yield the best results and the order was 1. Momondo (best by a country mile), 2. Skyscanner. 3. Google Flights. The more common sites (Kayak, Priceline, Travlocity, etc.) are pretty worthless by comparison. I recommend looking at itineraries on the top 3 above and then booking with Volaris or another discount Mexico carrier if they fly your route at a good price once you add on baggage and other fees. Carriers that make a PITA out of themselves by insisting on roundtrip tickets don't deserve your business.

We just finished booking one-way flights to the US, around the US, and back to MX from separate airlines.  No questions from United, Delta, or Volaris. We are RP with USpassports.

The OP was asking about flying on a one way ticket with a Tourist pass out of the U.S. into Mexico. No Mexican Resident visa was
mentioned.

I have flown US (Denver) to Guadalajara as a Tourist ONE WAY probably 5 times in the last 2 years, including about a month ago. Never a problem ever. Volaris, United.