Well jus' askin' the member won't achieve a lot.
"Are you a spy?"
"No."
"Can't possibly be a liar!"

And losin' one member is usually the better choice than havin' vital information given out that would bring big pain down on the alliance.
My entire alliance knows the location of the storage city in the alliance; I've done a great deal to keep it secret...but if our enemy found out, they coudl cripple it fast. I would happily prefer to lose one member than have the storage city attacked and all our spare resources stolen and all nearby defendin' cities barbed.
This has happened before on the previous storage city; I don't intend to let it happen on mine.

And I'm not even the host.

It's the same as real life...key information can't be stolen lest you risk losin' it.
Sayin' that, a lot of alliances will share information freely across the alliance, so anyone who is a spy can easily get access to it.
We share information based on a trust/rank basis, so lower rank (and I don't mean prestige rank) members, newer members or generally less trusted members can't get hold of important details, whereas long time trusted members can.

Although we're still at risk of spy attacks, it rarely happens and we have a handle on it.