BIK,
Two points;
1.If an overseas maintenance organisation is approved by their local authority FAA, UK CAA or whatever CASA has no say in how they conduct their work, years ago CASA had to approve these organisations not any more.The operater may choose to send a representative to conduct QA.
2. If an aircraft overnights at a port it may require a LAME to release it for the first flight of the day, hence LAMEs at some ports and not others, however it depends on the operater and how the maintenance manuals are written.
VTM