The way I perceived events was a bit between you two guys. XD The Tardis is not exactly alive though in Nu Who it is made of organic material. The Tardis has two very important functions, it chooses the location, usually, and it allows the Doctor to regenerate, as first mentioned by the 2nd in Power of the Daleks. The First, while dying, was saying basically nothing but, "I must get back to the Tardis" and the 2nd stated the link. Since then, every Doctor has died either in, or near the Tardis, Tom Baker having been the furthest away leading to the Fifth possibly having a 'failed' regeneration.
Too put any more emphasis on the Tardis is going too far, just keep in simple. I don't mind a bit of slapstick here and there, such as almost every room in the Tardis looking the same but my mind would snap if I saw the Doctor oogling the Tardis and reminiscing about first trips, the Tardis' favorite location, etc. XD
In essence, I consider the Tardis to have more 'mystic' qualities, where the audience is never completely sure that its alive or not, and I would not want to bring too much attention to this question.
Si-Fy and Fantasy, that is where my heart lies. To Doctor Who and its 18 years of brilliance, still waiting on the 50 yr anniversary!