Nobody would pay anyone based on the words 'im 25'. This is utterly ridiculous.
Which is why I said they might put plans in place, based on the info they've been given, and then officially verify it just before putting it into effect. That said, plenty of small employers with one or two staff members (little cafes, newsagents etc) wouldn't necessarily go down the full audit route and would take it on trust, having built up a good working relationship with you.
Back to the driving thing, I'm obviously far older than 25, but I work for a small charity and I've been asked on occasion to do a few errands using the van owned by one of the leaders. Nobody has ever asked to see my driving licence or a certificate of insurance with entitlement to drive borrowed vehicles - we have a great relationship and they just trust me to tell the truth or to raise any issues that there may be.
No what is patronising is to pretend that OP is a liar and that she's deliberately being fraudulent when it is obvious that isn't the case. It doesn't look like OP is trying it on in the slightest.
It depends on how you classify the word 'liar' - whether you mean a perpetual teller of untruths or somebody who lies just once. Like people who happily admit to getting very drunk every weekend but would take offence at being called a drunkard.
Assuming OP knows when her birthday is and can understand both the basics of a calendar and the standard way of calculating and stating your age across most of the western world, she did deliberately tell a lie. Not a groundbreaking nasty one, but as PPs have said, once you're found out to be so free and easy with the truth in one situation, people wonder if you're a habitual liar and wonder if they should trust anything you say. They don't know your motives or intentions: they just know that they asked you a very simple, basic question and you replied by giving false information.
your friend shouldn't have pulled you up on it in front of others and made you look silly.
Do we know the friend was intending to actually 'pull her up' about it? Don't other people innocently query information when it sounds like somebody might have been mistaken - if for nothing else, to assuage their own confusion rather than as a gotcha?