When a replica set member is configured with both arbiterOnly and priority = 0 (admittedly a weird combination), then db.isMaster() on the arbiter reports true for both arbiterOnly and passive.

Here's the replica set config:

myset:PRIMARY> rs.conf()
{
"_id" : "myset",
"version" : 1,
"members" : [

{ "_id" : 0, "host" : "Kilimanjaro:10001" }

,

{ "_id" : 1, "host" : "Kilimanjaro:10002" }

,

{ "_id" : 2, "host" : "Kilimanjaro:10003", "priority" : 0, "arbiterOnly" : true }

]
}
myset:PRIMARY>

Here's the result db.isMaster() on the arbiter:

myset:ARBITER> db.isMaster()
{
"setName" : "myset",
"ismaster" : false,
"secondary" : false,
"hosts" : [
"Kilimanjaro:10002",
"Kilimanjaro:10001"
],
"arbiters" : [
"Kilimanjaro:10003"
],
"primary" : "Kilimanjaro:10001",
"arbiterOnly" : true,
"passive" : true,
"maxBsonObjectSize" : 16777216,
"ok" : 1
}
myset:ARBITER>

The following four properties reported by db.isMaster() should probably be mutually exclusive:

ismaster
secondary
arbiterOnly
passive