From time to time, I hear these things from people who ought to know better.
Tone production and articulation are two different actions. Usually, we articulate the first note in a sequence according to the style of the phrase we are playing, but initiating the first note and articulating it are still two different actions, in this case happening at the same time. The air stream is continuous, and articulation consists of a series of brief interruptions of the air stream.
To develop a clean sound and full control of our embouchure and air stream, we practice playing without articulation. People often call that a “breath attack.” We use neither the tongue nor the glottis to block the air stream. We initiate the sound by starting to buzz our lips as we exhale.
The release component of the envelope of a sound is achieved by stopping the buzz of our lips or in conjunction with the attack component of the following sound. It is not accomplished by “plugging the hole” with our tongue.
You may have heard your elementary, middle, or high school band director (or a community band director) instruct the band to stop notes with their tongues when performing marcato or staccato passages. The reason school band directors do this is that they have a limited time to make a large group of unskilled musicians sound reasonably consistent. They don’t have time to teach each individual student the correct way to articulate. That doesn’t mean you should adopt the same technique in your own playing.
Articulation consists of briefly interrupting the air flow in such a way as to achieve effects like staccato, marcato, sostenuto, and legato playing. We can articulate using the tongue or the glottis. Single-tonguing is done using only the tongue, while multiple tonguing is done by alternating between the tongue and glottis.
You can also articulate using only the glottis. There is no minimum speed for articulation with the glottis. Therefore, there is no minimum speed for double-tonguing and triple-tonguing.
When practicing multiple tonguing techniques, a key goal is to play so that the listener cannot tell whether any give note is articulated with the tongue or the glottis. Every note should be consistent. The basic way to achieve this is to practice multiple tonguing techniques at a very slow tempo, and to build up speed gradually.
A general target for clean single-tonguing is to be able to play sixteenth notes with the tempo set at quarter note = 152 BPM. Therefore, there is a comfortable overlap between the fastest clean single-tonguing speed and the slowest clean double-tonguing speed.
When a player believes in this myth, it suggests that they never practice articulation with the glottis at a slow tempo. This is a common situation with young players who assume that multiple tonguing only applies to fast music, and therefore cannot be done at a slow tempo.