It can depend on the class/type of stock and also what sort of door or fault it is.
On more modern stock, there may be local isolation for specific power door controls, as well as remote unlocking/locking and overrides.
Obviously this may not be relevant in this case!
I think it can vary - I have twice been put in a taxi to complete my journey where it was specifically said to be "to home address". Ultimately, the contract one has with the railways it to reach X station
If there is a chance someone may share the taxi, or the town/village of the destination would not match a station address for audit purposes, it may be harder to get it to go to a home address.
It is also much easier to justify and verify why someone wants a taxi to a station on their ticket, rather than looking up everyones random street three miles away, to check that the railway replacement transport facilities arent being misused.
That being said, customer service skills on the day can be the practical solution, as well as basic set-in-stone TOC policies which may be part of a checklist for taxi ordering.