I agree with what you said.
English is 'both':
Dependent marking: case is restricted to a few pronouns.
He saw her. / She saw him.
Head marking: only 3SG.PRES is marked (plus be.1SG PRES/PAST)
I see the table / John sees the table
Therefore, English is
almost neither, but to the extent that it is one, it seems to be the other as well.
In terms of contrastive features, there's only:
Case: Nominative/subjective vs. Accusative/oblique
Agreement: either [±3SG], or [±SG, {1,2,3}]
Under a surface-level analysis, the complexity/extent of the marking appears to be roughly equivalent.
Arguable extra complexities:
--Genitive case in nouns
--1SG am/was [only] in verbs; [also, that agreement only applies in the present tense, except with 'be']
There must be something wrong with this particular data set in WALS or else I'm we're seriously misunderstanding what's going on.
Indeed.
Oddly enough, I wonder whether the better known languages might be less reliable in WALS. I imagine that the less documented languages simply say something in a grammar and it is coded into the database. Then for a language like English there is so much research and so many controversial ideas that perhaps the results are messier? This is obviously not acceptable anyway, but at least it would mean that to the extent that the maps are useful (which is, let's be honest, not really for English, Indo-European, etc. :p) and that we can rely on WALS for the languages we're not familiar with.
Or it could turn out that if it's this bad for English, it's just complete nonsense for the rest. I'm surprised though! Maybe we really are missing something, or maybe they really did switch the datasets...
Also, to be picky, the "no marking" category seems like it should be "word order only", and there should be a 4th (hypothetical) category "no encoding" or "pragmatic inference alone", which I doubt truly exists (no case, no agreement, no word order).
(Looking at the data there for Australia, where word order is often not much of a factor, I see no white dots. Dyirbal for example has case. Many languages have both. So it really does seem unlikely that a language would have no word order if it didn't have overt marking either.)
A 5th option could potentially be intonation alone, if that exists.
And what's "other" in this case? What's other than head or dependent marking? It's not neither, it's not both. I could understand "unknown" or "undefined".
Edit:
Looking at WALS again...
There is a place to submit comments. If our conversation doesn't make more sense of this, let's do that.
Looking at the two existing comments, I'm not sure I follow the logic in them either (the one on Salish is confusing, implying something about degree). Or maybe the issues we're seeing are just the tip of the iceberg.
Overall, one possibility is that this is just terminological. I'd hope they applied the definitions consistently, but it is possible that some are due to traditional classifications that don't actually match the data well. If "have" and "not have" can be interpreted as a sort of cognitive perception of the language, then who knows. What I mean is that we might not feel that agreement is "important" in English, so we could say it "doesn't have" agreement. That's a bad strategy, but could be the explanation. I'm still not seeing another.