It really isn't as cut and dried as that. I retired last year and worked in welfare rights for over 20 years.
I've had a few cases where the DWP has looked into spending capital, and things like buying a mid-range car, spending on necessary house repairs and having a a reasonably modest holiday have been deemed acceptable. Clearing or reducing credit card debt and a loan has also been considered ok, as has some spending on hobbies, and replacing things like washing machines and cookers, as long as they're not extravagant.
The test is "intent". If they think that someone has deliberately spent a shedload of money so that their capital is below the £16k cutoff, they can treat it as though they still have the money. If it's reasonable, and it's for something they need, that's fine.
One client of mine had spent £3k on a high end hi-fi system. He was a very isolated man with significant mental and physical health issues and music was his passion; the DWP didn't regard that as intentional deprivation of capital, nor his purchase of a fairly expensive bed, which he needed because he had dreadful spinal problems. I've also had the purchase of a £10k second-hand car disregarded.
It's a notoriously difficult area to give advice on, because what is "reasonable" is a judgment call and whether the "intention" behind the spending is deliberate "deprivation of capital" is really a matter of opinion. I suspect that the CAB adviser was giving the absolute worst-case scenario.
In my opinion, dipping into that money because you don't have enough to live on is unlikely to be considered intentional deprivation of capital. After all, if your income is so low that you would be entitled to UC if you didn't have the money from your mother, your income is below the level that the government deems necessary for you to live on. Therefore, you're spending to exist, not to get benefit entitlement.