btw the whole cant save deposit = cant buy is a poor generalization. It really depends on spending characteristics and this is why, ideally its better to get some of the furnishing before buying a place as then your spend pattern is a bit more normalized and biggish purchases are behind you. i.e. predictable margins of saving is clear. This is why banks usually look at your account over a period prior to giving a bond and/or rate. If however your spending, day to day (excluding once off lossy assets like funiture etc) puts you in a position which you can't afford to save then yes, i agree with statement.
Typically, difference between rent and owning per month is approx. 25-40% more pending levies (so levy, rates, building insurance.. assuming you already paying household insurance), excluding incidentals(garden = maintenance cost, 3-5yr maintenance costs like painting, annual roof maintenance checks, etc) which you need to save a margin for too.
Deposit basically, from what i've seen can either make a non approved bond approved (where the bank determined that affordability is in question) or is used to lure more preferential buyers (lowers risk on their side too).
1st time buyers who can easily afford it all costs associated with ownership i've been told easily still get 110% bonds from banks if you shop around, 2nd time or more buys ceiling is 95-100% though due to the risk added.