...They also pointed out that other cards have language similar to "Do X...if you do, then Y." and believe that if the designer didn't want you to draw a card on Domestication unless you had a card to meld, they would have used that language.
Correct. There is no conditional language on the card so there is no condition to be met. So the player with no hand card to meld will still draw a 1.
Conditional language is easy to spot:
...if you do...
...if you returned two...
...if it's green or blue...