When it comes to vertical drilling into a joist, the internet is split in two:
One is discussions about drilling a large hole through the joist to pass plumbing/electrical/etc, and the answer is "don't do it!". There's discussions about the bending face, thirds of the joist, code, etc., and how any notching/drilling on the bottom of a joist – especially in the center 3rd – is the worst thing you can do.
The other half is about mounting stuff to the ceiling – on which there are… crickets. If you keep looking, you'll find mounting instructions for stuff (like lamps, fans, bike hangers or these 400lb and 600lbs racks), where screwing (vertically) into the joist is what you should be doing (as opposed to mounting to drywall), and as long as you're centered enough on the joist, there's nothing else to worry about. Pilot holes are welcome.
Can anyone help settle the discrepancy?
Personally, I'm mounting a 6lbs projector (+2 lbs mount) in the middle of a long timber ceiling joist in the middle of a living room; the ceiling supports a residential floor (another living room) above it. Barring new information, I've decided to use 2 x wood screws (#10 or #12 w/ 1/8" pilot hole) instead of thicker lag bolts, since those should easily support the light, static load while minimizing displacement of the joist material.
Best Answer
I see your concern but there's really no discrepancy. The tiny pilot holes you will drill for your #10 screws to mount your projector do not remove any significant amount of material from the joist. They also don't go all the way through, just an inch or so. They won't significantly change the strength of the joist.
If you were drilling a 3/4" hole vertically all the way through the joist and running all thread through it, you'd be removing half the material in that spot, and that of course would weaken the joist significantly.
So where do you draw the line? I am afraid I can't give you an exact answer based on engineering calculations and testing. However I can give you a rule of thumb that has worked for me. I find that 3/16" x 3" pilot holes for 1/4" x 3" screws are adequate for anything you can hang off 2x framing, so there's no reason to go any bigger. That hole is smaller than the shaft of the screw but adequate to prevent splitting in framing lumber, and small enough that it doesn't significantly weaken anything.
I have mounted all kinds of equipment, often hundreds of pounds, using this rule of thumb without any problems. In the rare instances where I don't trust 1/4" hardware, rather than use larger fasteners, I'll use more fasteners; for example, sometimes I'll attach unistrut to framing with multiple 1/4" screws then hang the heavy stuff off the unistrut. This also distributes the load better.