No, it is not about the balance basically staying the same. The thing is, if the stock market (including dividends) got you 7% every year then you could withdraw 7% every year and your money would never end. But the stock market doesn't work like that. It could go -30% one year and +40% the next year. Or it could go 2% up five years in a row. If you happen to retire at the start of those five years and withdraw 7% each year then your money will go down a lot (20-25%). If in the sixth year the market goes up 20% then it's all fine, but if it goes down 20% then you're in deep trouble because now you only have 60% of your starting amount left.
This is why withdrawing 7% is not safe, even though on average, long term, the returns should be higher than 7%. 4% is the safe withdrawal rate as researchers have determined it based on past data. It means that even if the stock market goes down 40% or whatever happens, you should still be able to withdraw 4% of your original amount and expect that your portfolio will not run out in the next 30 years.