...The simple fact is that the instructions...(are)...WRONG. Therefore, the single point laser, when used for secondary adjustment in this way LIES!...
I don't think anyone will argue the point that the instructions provided with some economy laser collimators are often so simplified that the user will be hard pressed to achieve a reliable collimation. Check the one-step alignment procedure in the product description here
I think the problem is the conclusion that the laser somehow "lies". Used properly, the outgoing beam of a simple thin beam laser represents one thing--the focuser axis. As the focuser axis is one of the two axes that will be assessed and corrected when collimating a Newtonian, and it's one of the two alignments that have a defined performance tolerance, it's an important axial
alignment. If the internal laser alignment is good and the laser/focuser registration is consistent, there's no way the laser can "lie"--the outgoing beam is
the focuser axis.
Many users also adjust the primary mirror tilt to align the return beam back to the laser target (often visible in a side "window"). But the return beam is simply the reflection
of the focuser axis! If the focuser axis isn't precisely aligned to the center of the primary mirror first, using the return beam to adjust the primary mirror tilt will misalign the critical axial collimation.
A precision thin beam laser collimator coupled with precision mechanicals and used properly
is a valuable tool for axial alignment assessment and correction.
I suspect there is a conflict of semantics at play here.
1) "CENTERING" of the Secondary...(and)...2) "PRESENTATION" optimization...A simple "beam' laser most certainly WILL NOT aid in this endeavor; the sight tube or "holographic pattern" laser are the tools to use.
While I agree with this statement (and prefer a good sight tube for the job), there are still some users (and at least one manufacturer) who suggest using a secondary mirror reference spot to facilitate the alignment of the front end geometry with a simple thin beam laser. There are many pitfalls, complicated measurements, and convoluted "dead ends" associated with the procedure, but it has its following.
3) "AXIAL ALIGNMENT" of the Secondary is the process of adusting the tilt/rotation of the Secondary to aim the focuser axis at the center of the Primary...
Again, semantics--the secondary mirror is an optical flat and has no axis--although it reflects both axes when assessing and correcting the axial alignment. As described, the alignment is "AXIAL ALIGNMENT" of the Focuser
Since secondary mirror adjustments affect both
axes, changing the focuser axis this way also changes the primary mirror axis, which is why primary mirror axial alignment is always the last step.
The bottom line is that focuser axial alignment CAN be achieved irregardless of the state of "centering" & "presentation" condition of the Secondary, but that said, it's prudent to implement centering and proper presentation, BEFORE focuser axial alignment is undertaken.
If there are indeed beam-laser instructions out there that infer Secondary "centering" (and/or "presentaton") can be accomplished with that tool, it's the procedure writer who is mis-informing the user, not the laser.
Although their numbers are dwindling, there are still advocates--some use a secondary mirror reference spot, some don't...
This exchange reminds me of a quote by Wolfgang Pauli (after reading a young physicist's paper):
"This isn't right, this isn't even wrong."