You are wrong.
If you have a SIPP for example and you put money into it from any source you like they will automatically add the 20% tax relief.
But you need to make sure you only put in the max you are eligible for, e.g. 80% of your pre-tax salary (so that when tax relief is added it doesn’t exceed your salary), less than £40k, and assuming your MPAA (Money Purchase Annual Allowance) hasn’t been reduced to £2.8k due to being a non-tax -payer or being in taxable pension drawdown.
Tax relief is given when you put money in your pension and then when you take money out of the pension it is taxed (within certain rules) - that is how it is balanced - it has nothing to do with whether tax has been paid.
This should be obvious as putting money into your pension from a salary reduces the income tax you pay and additionally adds tax relief into your pension.
For example, one person could take tax-free money out of their pension after age 55 and put it into their spouses pension gaining an extra 25%. E.g. I could take £12k tax free from my pension when I am over 55 and put it into my other halfs SIPP and that £12k would get an additional £3K added as tax relief - this is all fine as long as my other half earns £15k per year. In this scenario I would be effecively gifting my other half £12k and she would be paying it into her pension and getting tax relief which is no different to her putting pre-tax wages of £12k into her pension and keeping the £12k from me.
Another example; someone on benefits that pays no income tax, can theoretically put £2,880 into their pension and get tax relief on it making it up to £3,600 - this money could be a gift from parents or simply savings from their benefits.