I presume that is in ballroom.
For Latin, Tango and Swing which are all mentioned: Simply not true. Your hips are so far apart that it doesn't matter.
That being said: you ideally have a key/change pocket in your pants. Or even better, a beltline interior pocket. The latter is where I keep my keys when dancing tango. On the right side btw. You can't tell from the outside.
These pockets are sadly not available in off-the-shelf clothing any more since maybe around the 1940's.
The reason is twofold: you won't feel your keys/change as much and from the outside you wont have anything ruining your leg's silhouette. Left or right. :-P