You pretty much just answered the original poster's question by them sticking
with the metrically compatible Liberation Serif/Tinos fonts to type the paper
and if it has to be sent digitally, change the font to Times New Roman, save,
and send. You may not have it installed, but it will show up to any user that
has it installed.
If the paper has to be printed, it can create an issue if the font doesn't
match Times New Roman even if the font is metrically compatible. Like someone
said earlier, FreeSerif is one of the best looking Serif fonts that comes
close to the look of Times New Roman even if it isn't exactly metrically
compatible as Liberation/Tinos.
How can this be fixed for the future? The FreeSerif devs actually pride
themselves in not being a Times New Roman clone but if a student uses it, we
don't want another 60/100 grade scenario again.
If there is no compromise for the font according to the teacher and it must
be printed, should the student type the paper in Liberation/Tinos, install
the Times New Roman font, change the font to Times, print the paper, and then
remove the Times New Roman font immediately?