Well. Decline in giving full API to check is a good thing for me as one of recruiters.
Using corp policy "full API is needed" i easily drop part of my job and have more time to play instead of checking, interviewing, training and supporting newcomers

So guys. Pleeease. The more people hide their APIs the more time i can spend to the game

And on a serious note. Yes, i know that properly fitted spy won't be caught by API. This measure is just a simple locker on your door. Everyone knows that there is no unbreakable locker exists. What was built by people can always be destroyed by people.
However no one will have his door unlocked and opened just because of this principle.

So the full API, KB, forums and google checks are locker on your door. Will stop lazy unskilled and not-determined hacker. Or just person you would not have in your corp. Some possibility for random mistake from spy as bonus.

There is one more thing exist. If you know almost everyone from your corp by real Name, where he lives, who is he in RL, etc... you will not want strangers came to this group. So newcomer will have many personal questions. After all you need to trust a little to your corpmembers. And if you are "too hidden" you have significally less chances to get into this group of people. This is just like in RL. Nothing really differs. "Internet space pixels" you say? Nope. This is time spent to make something, team work, real effort, real money maybe.

It's not even a full api request, it was for an incredibly limited api (character list\skill sheet).
I'm trying to get my head round the mind set of it all and in all honesty, I'm struggling.

The question still stands though, how do you filter for spys?

oh and bar "reading my eve mails" I've not heard much that makes me buy into this "OMFG API AAAHHHH"

Also, what corp pos thing?

Unless you are a spy you don't need to be paranoid about giving your API. They CAN NOT get into your account with your API.

aside from API:

forum search - special attention to character bazaar and Timecode Bazaar.
checking employment history - maybe there are some alt corps in there? evewho is great for this sort of thing
checking contracts history - not complete but it might give you some pointers
checking killboards - who did he fly with? who did he kill?

If you have your own spies inside entities that you suspect to spy on you you can also do interesting stuff like

* watermarking important forum posts/announcements to trace leaks (look for the PL forum mirror it has some nice info on this: idea is that you display different versions of the same post to each viewer, e.g. by automatically replacing some characters with equally looking but different unicode characters based on the viewer's forum userid; or by offering different combinations of synonyms - e.g. four words with one possible synonym for each gives you 16 different versions of the forum post which already cuts down the number of people you suspect of having leaked the post considerably)

* harvesting IPs, e.g. post a link to some funny image hosted on a server you have access to on your enemies' forum, log IPs & timestamps which access that image, try to connect them to characters that replied to your post, compare to your own people's IPs that you harvested through your TeamSpeak server.
(or have your spy post a link to your file during some roam, that way you know pretty well who has clicked it, try to correlate IPs with characters by e.g. using the country information displayed by TeamSpeak; If there is only one German in the roam the German IP is probably him).
Also use voicecomms logs to look for people who listen in on ops but don't participate (or people who only log in for pvp ops). Check IPs that access your own forums or voicecomms for obvious proxies/VPN providers.

* make note of idiosyncratic misspellings or grammar fails

* keep a close eye on people who are too eager to x up or never x up when you call for all spais to 'x' up in fleet chat.
j/k

* ...

In general kicking a spy will only result in him being replaced by another one that is harder to detect.
My advice would be that unless you suspect one of your FCs or directors/CEOs to spy on you, don't bother too much about it.

not trolling, genuinely want to know as I'm failing to see the other side of the coin.

Some people just take this game too seriously.

well. you have never had situations when your enemy knows every ship, fit and move of your fleet?
I have had it few times. This is real pain i would say. When you loose battle before start just because of some ****** spy in your corp/alliance. When your every command on comms is known to your opponent.

Maybe some day you will understand it.... When you start to play MULTIPLAYER Eve and not only INCURSION Online.

Big alliances want api key's because: they like fishing.

I got purged from renter corp cause ex PL guy gave me 1 isk