Your Question: do regulations permit flying a 737-800 with passengers for that distance (1:44) with only one pilot under these circumstances?
Answer: I'm unable to locate, nor would I expect to find, any exceptions or exemptions under Canadian or U.S. regulations that would allow operating a B737-800 (whether carrying passengers or not) with a single pilot. According to the requirements specified in the FAA Type Certificate Data Sheet (pertinent excerpts shown below) the B737-800 requires a minimum flightcrew of 2 - a Pilot and Copilot.
The reason the airline flew the airplane to a nearby Canadian airport before departing to its destination in Mexico may not have been clearly explained to the passengers. Nevertheless, it is beyond improbable that the B737-800 would have been flown by a single pilot.
The FAA Type Certificate Data Sheet (A16WE), which includes the B-737-800, shows the following excerpts:
RE: page 1:
RE: page 33:
(highlights/underlines in both images are mine)