More than 40 years ago, short, medium and long term referred to daily, weekly and monthly data. By the 1980s, the time frames evolved to hourly, daily and weekly and in the recent decades, even as short as ticks.
Bollinger studied the evolution of trading bands, starting 100 years ago with LeDoux's ROBOT charts, Keltner's Ten Day Moving Average Rule (1960), then Donchian Channels, Hurst's curvilinear channels, and Schmidt's percentage bands in the 1970's. All of these were symmetrical band systems.
In the 1980's, Marc Chaikin and Bob Brogan developed BOMAR bands (Bob + Marc), the first adaptive bands which let the data set the band width. Around the same time, Jim Yates created something similar by utilizing option implied volatility.
Then along came Bollinger with the idea that standard deviation could be used in combination with a moving average to provide a more reactive indicator than most of the above.
Bollinger tested a variety of combinations of moving average and standard deviation. He found that with a 20 day moving average, two standard deviations encompassed 90% of the data. When the length of the moving average is shortened, the number of standard deviations must be reduced to maintained the amount of data encompassed and vice versa for longer term moving averages.
Therefore, the default is a 20 day moving average with 2 standard deviations with up or down shift according to the length of the moving average. But given the changing nature of the market as well as trading time periods used, this is a starting not an end point. Even Bollinger recognized this 20+ years ago and recommended adjusting standard deviation length accordingly.
Fidelity got the answer right but not for the reason implied. It's the moving average length that dictates standard deviation size not some arbitrary choice for the number of standard deviations.
Source: Bollinger on Bollinger Bands by John Bollinger