Being super accurate setting points is doable, it just takes lots of time. My crew has in the past, set verifably accurate column lines, bolt anchors, etc at accuracies of BETTER THAN 0.01 feet. Did we use a total station, nope. we didn't
When you have to be REALLY accuate, get out your chain, plumb bob, and 1" theodolite (yeah, you know, the old ones), and factor in temp correction, take your time, and boom, you have a building that closes in the thousandths.
We sometimes monitor large/long walls for movements, and often times have to detect 0.01 movements.
so sure, we can make it accurate, but more than likely, your shots of the 'surronding' buildings aren't going to be good enough . It can be very difficult to survey existing structures because they are very rarely straight up and down. Also, make sure your geotechnical engineer is involved early on. If you have building really close together, you should tie them togetther so they settle as a unit, as opposed to 'floating' and running into each other.
Cheers.
NUMA, PE