Leaving Mexico after 90 days as part of ESTA requirements

[S]omeone at the airline told her that because she touched us territory with the 3 hour layover done in the us, she is still under ESTA laws and needs to leave Mexico too, before 90 days instead of 180.

This is not correct. The 90-day rule for the Visa Waiver Program only concerns travelers who wish to re-enter the US within 90 days after entry. Border officers are permitted to readmit them for the duration of the initial 90-day period instead of granting a new 90-day period. A traveler who seeks to re-enter the US after the expiration of the 90-day period can only be granted a new 90-day period (or be denied entry, of course). Since your plan is to return to the UK without transit through the US, you do not need to worry about that.

In no event can US law control when someone in Mexico is required to leave Mexico, of course, and the US will not keep track of your fiancée's travels after she flies to Mexico. In particular, it will not know when she leaves Mexico.

Furthermore, the answer to your question …

[Will] going back to the uk in a direct flight, even after her 90 days of Esta are done, … reset her clock and allow her to enter the us in the distant future[?]

… is yes. The only potential problem would be if she arrived in the US from Mexico, Canada, or the Caribbean, but if this truly happens in "the distant future," the chance of such a problem is virtually nil.

For reference, the regulation that creates the "clock not resetting" rule is 8 CFR 217.3(b):

(b) Readmission after departure to contiguous territory or adjacent island. An alien admitted to the United States under this part may be readmitted to the United States after a departure to foreign contiguous territory or adjacent island for the balance of his or her original Visa Waiver Pilot Program admission period if he or she is otherwise admissible and meets all the conditions of this part with the exception of arrival on a signatory carrier.