U are assuming I make assumptions....
There are different modes of valuation namely indicative, desktop & formal valuation whereby the first two modes are probably like you mention, more art than science. This is why it may differ from valuer to valuer because it simply is a "chop chop" type of exercise. Since formal valuation cost $$ and customers love shopping around for rates, the mortgage sales usually just rely on indicative and desktop valuation in their initial assessment, hence the discrepancy from bank to bank.
However the actual credit decision will have to be backed up by a formal valuation whereby the valuer is to do a site visit to look at the actual facing, interior layout etc... When the formal valuation is issued, it really is up to the Bank to stomach the "risk" if the value is significantly lower than the purchase price and the customer is asking the bank to match. This really depends on the bank's risk appetite (amongst a whole host of other factors) at that point in time. If the bank at that point is already "over-exposed", they will not stomach this risk and there is not much point for them to do another formal valuation.
However sometimes when a bank is desperate or they value your business so highly, they may just decide to stomach the risk. It doesn' mean that the valuation has changed. It's a case that the bank has a bigger risk appetite at that given point in time.
Anyway this is my two