This is how we tend to describe what we do, but to be honest it isn't that good as a descriptive label as we rarely 're-enact' anything directly. Mostly what we do is try to give people as good a flavour as possible for our historical period as we can. Inevitably in re-enactment a number of compromises need to be made, whether because the research evidence doesn't exist to tell us how something was, for health and safety reasons or simply sheer impracticality or expense of doing something that was common in period but is now no longer possible. Also we now know quite a lot more than our predecessors and sometimes we don't want to repeat their mistakes.
Despite all this we do our best to get as close as practicably possible without endangering anyone's life or health. Our group tries to follow evidence where it exists and to look at as many period sources as we can to reproduce things faithfully and accurately.
Perhaps the best labels could well be either historical interpretation or perhaps experimental archaeology.
It should also be mentioned that 're-enactment' is a very broad church and that the standards of what is acceptable vary dramatically from group to group and even within groups. Even the largest groups will have people within them that could be teleported into their peirod and not stand out too much whilst simlultaneously having people that are 99% modern with nary a natural fibre about their person. It is mich easier to get very high standards of accuracy with a small committed group who are passionate about their hobby than with a larger amorphous mass that are there primarily to see their friends and have fun regardless of the history1).
All this of course is merely my personal opinions.