They can be--and that's the most damning evidence against this. Magnetite is a magnetic mineral that is frequently not melted by magma. It also forms long, skinny crystals. If there's flow to the magma, this actually orients them according to flow (either parallel or perpendicular to flow direction; think sticks in a stream). You can therefore look at the orientiation of these crystals by examining the magnetic field--and what you see is orientation according to flow. Saw a talk on this back in college, using Stone Mountain , in Georgia as the case study (the guy was from Atlanta, so it was an easy choice). This was tested on a few different intrusive igneous formations, including several where other evidence for flow was available, and proved to be fairly robust, if limited in utility (you need magnetite for it to work, and strong enough flow to overcome the mineral's tendency to orient itself to Earth's magnetic field).
If Haig was correct, we would expect to see magnetic crystals suspended in fluid significantly shifted during the cooling process. Magma flow is not the fastest thing in the world (literally in this case!

), and the Earth's magnetic field isn't exaclty super-strong. Regardless, anything that is strong enough to affect tectonics must be strong enough to affect mineral grains. Likewise with volcanoes--they are basically intrusive melts that get exposed, after all, so anything that can affect them must necessarily have substantive and detectable effects on orientation of magnetic minerals. And the simple fact is, we don't see that--we see minerals oriented by the Earth's magnetic field, and by flow. (The two concepts are not exclusive; last I heard it was hypothesized that Stone Mountain was involved in some local volcanism, so if Haig was right we should definitely see evidence of it in these formations.)
There are other reasons to believe this to be nonsense, but this is direct experimental evidence disproving this entire concept.
Quite obviously the orientation of minerals falling out of suspension along the sea floor would likewise be a direct experimental test of this idea, but I can't think of any specific studies focused on them off the top of my head. I do know that the pattern shown in the magnetic polarity of the sea bed is explicable by polar reversals, and that there's no indication that I'm aware of for any solar cycles expressing themselves in the material. Placer deposits are another place to look, and have the added bonus of providing detail down to the scale of years, if not smaller (depends on the formation).