Only gods and angels can speak Supernal so that all may understand.
Your quote is from the Dungeon Master's Guide (page 171) then re-phrased by the Rules Compendium (a more up-to-date version of the rules), which actually says this:
The gods have their own language, Supernal, which they share with their angelic servants. When a god or angel speaks Supernal, it can choose to speak so that any creatures that understand a language can understand this divine speech, as if the speaker used their own languages. Immortals that speak Supernal can understand speech and writing in any language. [RC69]
The Rules Compendium then goes on about the issue of PCs learning Supernal (again, re-phrasing the DMG's opinion on the matter):
Adventurers don't normally know these languages [Supernal and Primordial] to begin with. They might eventually learn the basics of communicating in these tongues, but without mastering the words of power. Similarly, mortals who learn Supernal don’t gain the ability to have their words universally understood, but they do learn to read the Supernal script and to understand immortals speaking in that language, even if the immortals have not chosen to make themselves understood to all listeners. [RC70]
This raises an issue which is relatively unusual in 4e: "Immortal" is a mechanical keyword with a specific definition (you are considered a native of the Astral Sea), while "mortal" is not a corresponding keyword--or, in fact, any keyword at all. And unless/until a character without that keyword gets an actual bit of rules text saying "You are considered to be an immortal creature," he's not.
immortal: Immortal creatures are native to the Astral Sea. Unless they are killed, they live forever. Examples: angels and devils. [RC 60]
"Mortal" has no definition, and while defining it as "not an immortal" seems logical, it doesn't mesh neatly with other established creature types like "elemental." This is something your group will have to figure out for itself. (I would rule that "mortal" in this particular case be treated as meaning "not an immortal," but without that interpretation setting any precedent for the meaning of "mortal" in other contexts.)
It is possible to start play as an immortal (by being a Shardmind or a Deva) or to become an immortal through various character advancement options, in which case a GM would probably allow that learning Supernal grants you the ability to understand speech and writing in any language because "you are considered to be an immortal creature for the purposes of effects that relate to creature origin." However, you still wouldn't be an angel or a god, and thus couldn't choose for your Supernal speech to be understood by all.
There are also a handful of powers and feats (including the Platinum Templar paragon path level 12 utility power "Bahamut's Voice" and the Paragon Deva feat "Remembered Mothered Tongue") which let you speak Supernal as if you were an angel or a god under specific circumstances.