Hey, so far as I know, all healers are technically not limited to magic damage; I think if a scholar smacks someone with their book for the auto-attack, it's counted as physical for purposes of damage calculation.
More seriously, yes, the parameters are—so far as I can tell—somewhat convoluted. Weaponskills can situationally deal magical damage, as we know from Red Mage, and I suspect that spells can situationally deal physical damage; though I cannot think of a concrete example of the latter, it would make sense for it to be possible in the system given that we know the former is.
And based on how the combat system used to work with regards to aspected damage, I strongly suspect that it's possible for things to deal both physical and magical in the same attack, architecturally, whether or not that's presently used. Which would mean that the final damage communicated to the client not only wouldn't show whether it was magical or physical, but you actually couldn't say either way.
To use the example I gave earlier, think of a D&D campaign. Say the party's paladin has a longsword+3; that gives a +3 modifier to the normal sword damage (as well as to the attack roll, but that's not relevant here), so the sword does 1d8+3 slashing damage on a successful attack. Now let's say the paladin has a holy rite that lets them empower the weapon for 3 rounds of combat provided they land a hit each of those three rounds; failing to attack or failing to land a blow instantly ends the blessing. During that time, the weapon also does 1d6 radiant damage.
Let's say the paladin lands a blow. But the thing they're fighting is evil and has vulnerability to radiant damage, so takes double radiant damage. The paladin rolls 1d8 for the slashing damage of the sword and gets a 4; since it's a +3 longsword they do 7 damage. Then they roll 1d6 for the extra radiant damage, and roll a 4. Since the creature is vulnerable to radiant damage, they take 8. That's a total of 15 damage.
But the thing is, the DM calculates the resistance or vulnerability to damage types—handles mitigation, as it were—and then just subtracts 15 from the creature's hitpoints. The DM doesn't separately write down that it was 7 slashing and 8 radiant damage.
Or in other words, the damage is presented to the thing shown to the players (if the DM has hitpoint bars on enemies on Roll20/Fantasy Grounds/whatever) as "You did (1d8+3)+(1d6*2) damage to the creature", instead of "you did 1d8+3 slashing damage to the creature, and also 1d6*2 radiant damage".
And my strong suspicion is that whether or not the FFXIV combat system currently supports a single action causing more than one damage type, the fact that at one point it probably did means that the server probably only communicates to the client "<Actor> does <Z> damage to <target> from <action>", rather than "<Actor> does {<X> physical damage, <Y> magical damage} to <target> from <action>". Especially since if I remember right from waaaay back in the beginning, I think magical damage was not only aspected (hence the 'unaspected damage' we still have in tooltips), but also physical damage was internally aspected (slashing, piercing, etc.); that'd be a lot of potential damage types.
But also I'm running on "before you speak to me, if you value your life you will bring an offering of coffee" levels of sleep deprivation (and I don't even like coffee), so I'll grant my off-the-cuff recollection of 2.0 may not be perfect; I'm not 100% certain I can remember last week at the moment.