No, that's not the reason. It's because the solubility of a gas in a liquid decreases as the temperature increases i.e. the opposite of the solubility of a solid in a liquid which increases with increasing temperature. So when you take the vial out of the fridge and let it warm up slowly any dissolved air or other gas that has been used to flush the vial during manufacture, comes out of solution in the insulin into the gas space at the top of the vial or as bubbles formed when the vial is shaken as the reservoir is filled. If you don't let it warm up properly, that dissolved gas gets transferred to the reservoir and then comes out of solution as bubbles later.
As to the 28-day 'rule', the very rough rule of thumb that chemists use is that the rate of a chemical reaction doubles with every 10 degree rise in temperature. So if you keep the insulin in the fridge at 4 deg and then take it out to a warm room at, say, 24 deg, the rate of degradation of the insulin (which is a chemical reaction) will increase four times. There are most likely other effects that also affect the degradation of the insulin when you start using the vial, such as the effect of introducing air into the vial as the insulin is taken out. The loss of insulin activity is gradual so that at the 29th day it won't suddenly stop working, but as time goes by its effectiveness will be more unpredictable. Best keep to the rule.
Personally, I don't keep it in the fridge after it's been started when I'm in the UK where we don't usually have temperature extremes. But when I'm in a hot climate, I keep it in the fridge and let it warm up for a bit before use.