I began a rewatch a few weeks ago, and recently got up to Season 3. During 'Flashes Before Your Eyes' there is a scene where after Desmond is leaving his interview with Widmore. He takes his tie off and sees Charlie, He walks up to him, trying to remember where he knows him from. the dialogue is something like
'I know you! How do I know you?
There was a hatch!
I remember seeing you, there was a computer and a button
We were on an island....'
And so on...
But at this point, Desmond has only interacted with the losties for 5 hours or so,
When John turned up, Desmond ran away and wasn't seen again until Shannon's funeral.
During that time, no one really referred to the 'hatch'.
Desmond was taken in by Kelvin, Kelvin had joined Dharma and must have been in the swan with Radzinsky during the purge and Both of those would have referred to the places as 'Stations'.
Desmond uses the term 'hatch' a number of times.
In Orientation 'Marvin Candle' says :
'Welcome, I'm Dr. Marvin Candle, and this is the orientation film for Station 3 of the DHARMA Initiative'
Meaning each site was referred to as 'Stations'
Kelvin would have used the term 'station' or 'bunker' not 'Hatch' from his perspective it was 'The back door'
Desmond should have said 'There was a Station' and would of used this term in preference to 'hatch' as this was a Lostie term and he would have described it how using the terms told to him first.
Sorry if this has been brought up before.