I'm not seeing that much difference between the public sector and listed companies - in both cases you are using someone else's money and you have an obligation to get best value for them - and to be seen to get best value. If there is a conflict of interest you should normally remove yourself from the process whether in the public or private (listed) sector. There may be very occasional times when a person with a conflict of interest needs to be part of a procurement process (e.g. they are the only available subject matter expert) but the nature of the conflict should be declared and everyone else involved should be careful to probe that conflicted person's contribution to the process.
It is only if it is your money, either as a private citizen or because you own 100% of the company, that you can do as you please.