While the government is making gradual changes the requirements and checks for UK citizens to claim job seekers allowance week after week are laughable low compared to the rhetoric thrown around.
I recently spend five months out of work and unable to find a job and received welfare. I saw others like me playing the system. I saw others like me struggling to satisfy the system and more, applying for everything and getting rejections similarly. The system doesn't differentiate between the two.
To some degree it's the old 'where do you draw the line' - do you prefer to see the innocent suffer or the guilty go free?
In a system where the individual can decide where to put the money, everybody can decide who is deserving of help.
If you mandate wealth redistribution, you need to create a complex ruleset that decides who is eligible. The rules are established by the ineffective and opaque processes of politics and government.
The resulting system is more complex, more expensive and easier to game.
Basic income still has the problem that people get my money who do not deserve it in my opinion.
Over a certain amount of income earned however, the benefit becomes negligible.
This type of thing (even when it involves fire protection) is redistribution. One set of people are taxed to pay for things, another set of people get the benefit -- even if it is the same set of people the distribution of the tax and the benefit aren't the same, and the difference is redistribution.
Note that I am not saying this is undesirable, merely that it clearly is redistribution.