I think Draco's wand chose him, although I do see what you're saying about parsing the language. Draco demonstrated throughout the series that he knew exactly what he wanted, that he wanted the best, and that second-hand supplies and clothing were unacceptable. For example, Draco got all new clothes and robes, a Nimbus 2001, the Hand of Glory, and weekly boxes of sweets and treats from home. I would imagine Draco would have pitched a fit if he himself didn't get to be choosen by the perfect wand. Further, in Deathly Hallows, he was extremely motivated to get his wand back from Harry after Harry won it from him, to the point that he follows Harry into the Room of Requirement.
‘That’s my wand you’re holding, Potter,’ said Malfoy, pointing his own through the gap between Crabbe and Goyle.
‘Not any more,’ panted Harry, tightening his grip on the hawthorn wand. ‘Winners, keepers, Malfoy. Who’s lent you theirs?’
‘My mother,’ said Draco.
Deathly Hallows - page 505 - Bloomsbury - Chapter 31, The Battle of Hogwarts
Draco's wand served him well, which indicates, I think, that he and his wand were paired up nicely. Draco, for all his faults, did show some formidable skill in spell casting and duelling.
I think if Draco was using an heirloom wand or a wand just picked out for him by his Mummy, his skill would not have been as strong. Both Neville and Ron, who had hand-me-down wands, did much better at magic when they were able to get a new wand, a wand that chose them individually. According to POTTERMORE, unicorn tail hair wand cores -- which Draco's is -- tend to form a very strong and loyal bond with their owners and are difficult to sway their allegiance to a new owner. Also, interestingly, wands with a unicorn tail hair are the least likely to turn to the Dark Arts, and we all know that in the end Draco was unable to stomach being a Death Eater.