'When I read about music theory on the internet I sometimes come across the circle of fifths. I don't see you mentioning the circle of fifths in this method, don't you use it?'
The circle of fifths is a system to calculate how many, and which, sharps (#) and flats (b) a key exists of.
SV Method indeed does not use the circle of fifths. By using the sticker you actually skip the use of the circle of fifths. That is because with the sticker you're thinking in intervals, and not in specific notes. Because of that it doesn't matter if you play, for example, in C, Eb, A or F#.
First of all, it saves you a lot of thinking.
Another advantage is that it makes you more independent of keys. You reason from the sound that the intervals give than from a key.
Because you think in intervals in stead of in notes - except the root note - you can play these more conscious. You look at the function of a note in stead of the note itself; the function is the interval. An interval always sounds the same, only higher of lower according to the root note you use.
Example: the note c is the 1. Play the 3. The note d is the 1. Play the note 3. The sound the 1 and the 3 both times gives is the same, only the second time the overall sound is higher.
Because of that you can directly see the chord-tones in a scale at different positions, regardless of the key. You can also switch fast between different scales.
The video below first explains about the circle of fifths and after that deals with why it isn't used in this method.