I just had a second battle with the same army vs 2 black widows.  They again tried to web my archer, and after that cast beguile on the archer.  Beguile affects melee attacks not ranged (at least, that's what the spell description and my ingame experience shows).  So, it's not just web that's being misapplied, it's other spells/attacks.  I'd like to see the AI addressed to fix all of this, at least eventually (come on Frog, hire a[nother?] full time AI programmer!).  Meanwhile, your fix is a good one 

I am using the Panca Archers from the quest (save the village or something?).  It's too early in the game to have researched the archery tech.

It's a huge world, insane world and insane AIs, most of the choices at maximum (resources, mobs, quests, etc.), and my custom kingdom sov vs 6 AI empire sovs (the 4 default and 2 I created).

Just fought a corpse spider (from the rat quest).  Repeated the battle twice (so 3 total), and in the 3 battles it webbed a melee unit (the militia we start the game with) twice and my sov once.  This was against the same army (with the Panca Archers) so the corpse spiders' targeting seems ok (from the admittedly small and anecdotal sample), and different from the Black Widows'.

Would the black widows have different targeting priorities, perhaps due to different abilities?  That different mobs would have different targeting priorities is a good thing, as long as they don't do 'stupid' targeting (and webbing ranged units would seem to fall into that category).

EDIT and yes, that web would adversely affect initiative is logical and would be a good fix (apart from the 'web ranged units' fix)!

Webbing ranged units is far from stupid, prevents them from kiting all over the map. When I have a pure ranged army with lower defense, web can ruin my day. Problem is the AI doesn't understand this, that spider is probably seeing the archer as the weakest unit and so it's directing its attacks at it, doesn't matter which attacks and doesn't matter if it can reach that unit or not. Compounding the problem is the fact that the spider will not move at all while using web and beguile, so instead of say running right up to the archer then webbing it so it can eat its face next turn, it casts web from the other side of the map then gets combat locked by melee next turn, or takes two turns to reach its target giving it time to potentially break out and run away.

Without making the AI smarter, a much better fix for AI spiders would be to make web and beguile 1 range melee attacks that do full damage in addition to their effects. Until then spiders are going to be the easiest monsters on the map because you basically get two free turns to kill them before they start fighting back. They could then add another web ability that's ranged that the AI isn't allowed to use, until it's smart enough to do so without wasting a turn.

The AI seems to regard webbed non-melee units as disabled, as if I have spiders and web enemy ranged units or casters, they skip their turns (won't fire arrows nor cast).  If I move a unit next to an AI melee unit that has been webbed, though, their melee unit will attack.  This is persistent from FE.