There is a reason why Fitbits are not allowed in sensitive US military facilities and it appears they should not be used at secret US bases either:

A portion of the Strava Labs heat map from Beirut, made by tracking activities.

An interactive map posted on the internet that shows the whereabouts of people who use fitness devices such as Fitbit also reveals highly sensitive information about the location and activities of troops at U.S. military bases, in what appears to be a major security oversight.

The Global Heat Map, published by the GPS tracking company Strava, uses satellite information to map the location and movements of subscribers to the company’s fitness service over a two-year period, by illuminating areas of activity.

Strava says it has 27 million users around the world, including people who own widely available fitness devices such as Fitbit, Jawbone and Vitofit, as well as people who directly subscribe to its mobile phone application. The map is not live — rather it shows a pattern of accumulated activity between 2015 and September last year.

Most parts of the United States and Europe, where millions of people use some form of fitness tracker, show up on the map as a blaze of light, because there is so much activity.

In war zones and deserts such as Iraq and Syria, the heat map becomes almost entirely dark — except for a few scattered pinpricks of activity. Zooming in on those brings into focus the locations and outlines of known U.S. military bases, as well as of other unknown and potentially sensitive sites — presumably because U.S. troops and other personnel are using fitness trackers as they move around.  [Stars & Stripes]

You can read more at the link, but in most cases using a Fitbit to run around Yongsan Garrison is not going to provide valuable intelligence information.  However, if there is a bunch of Fitbit activity noticeable in an isolated area of Africa for example, it may be a tip off there is a secret US military base there.  That is what is driving the concern.