This is 100% correct. EVERY new licensee is issued the next sequential call sign for that zone. If you want a vanity call, you have to first get your license, then apply to change.
What you were told is not fully correct. Yes, they stopped sequentially issuing call signs according to license grade years ago, but there have not been dedicated call signs "per license level" for many years. This means there is no such thing as an 'Advanced' or 'Novice' call sign format anymore. The current format for a new licensee, regardless of grade, is xxXxxx.
There are certain call sign formats you need to be AE to apply for, but none of those are new calls and are recycled from dead people and people who failed to renew for 2 years, thus giving up their right to retain their call.
Even at that, xXx, xXxx and xxXxx calls are very hard to find, in the sense that anything decent (easy to key, easy to say, cool, unique, etc.) is snapped up if/when it ever becomes available. There is also a preference system, in which you would get first dibs on your deceased father's call sign for example.