A scalar value is interpreted as TRUE in the Boolean sense if it is not the null string or the number 0 (or its string equivalent, "0"). The Boolean context is just a special kind of scalar context where no conversion to a string or a number is ever performed. (see perldata)
I know what you mean by the null string, but not every one does, specially not the people who need a reference. Perl doesn't have the concept of null, and we avoid using the term null string, because it's not always clear what is meant by it, the empty string, or an undefined value.
Having said that, you only list three things that are false in boolean context: the empty string (null string), the number 0, and the string "0". But you left out the most important one: the undefined value. But there are more, here's a (hopefully) complete list:
When used as a number, undef is treated as 0; when used as a string, it is treated the empty string, ""; and when used as a reference that isn't being assigned to, it is treated as an error.
Well, there's also auto-vivification.
The while statement executes the block as long as the expression is true (does not evaluate to the null string "" or 0 or "0"). (see perlsyn)
I wonder why you mention while, but not for(;;) or until. Having said that, your statement is close, but not completely true. The block can also be exited with a last, return, goto, die or even a next LABEL_TO_OUTER_BLOCK statement. Furthermore, if the condition becomes false during execution of the block, the execution isn't stopped - checks are only done before entering the block. Finally, there's
which will execute the block at least once, even if the condition is never true.