For the most part - this is standard butthe details for all carriers are going to vary.
For example, if you are at LHR, the answer is NO because it will take too long to get through security and out to a distant gate.
At LTN the distance is shorter and they might say yes to hand luggage only.
At STN you have to use the shuttle and that might intorduce too long a delay.
The use of the phrase "The captain's decision" may - or may not - be a ruse as it sounds better than, my supervisor's decision. Because, naturally, you would then ask to speak to the supervisor, whereas you know that you cannot speak to the captain!
Also, the cost to a carrier of missing their slot is enormous.