"That many" is referring to the actual number of cards you discarded.
Yeah I don't think there was any question about this; we all agree. The only question is whether or not the other incorrect reading was obviously wrong from the wording alone.
I'd say that technically it is ambiguous. The first edition text, ironically, was less ambiguous, since it actually specified "+1 card per card discarded", while with the current reading it can be interpreted as
- Choose a number X
- Discard X cards
- Draw X cards
And by the usual principle of "do as much as you can", if X is larger than the number of cards in hand, you'd just discard as many as you can and then draw X (or as many as you can if X is larger than the number of cards in your deck). The only question is whether X is "up to the number of cards in your hand" - obviously the intended meaning, but not technically spelled out