I would want to know:
a) had he ever guarded against humans
b) has he ever shown anxiety about humans handling foood/toys around him
c) depending on the answers to the first two, do you have children in the home (as residents or guests)
...and since your update I'd now want to know more about why they want him exercised away from other dogs.
If he has guarded against humans, your management of him would need to be much tighter than if he hasn't. Labs are often scroungers and you need agreed methods of dealing with it when he gets something he shouldn't have and is dangerous to him. Ideally you need the kind of tight management where he nevers gets it to start with.
If he shows signs of anxiety around humans handling items of value, he needs consideration and patience so that it does not get worse and - ideally - gets a bit better with the humans he trusts, at least.
If you regulaerly have children in the home and he shows active guarding against humans, I would reconsider. It can be done, it's hard work and it puts too big a risk there (IMO) right from the off.
Why does he need to be exercised away from other dogs?
There are a lot of variables here, too many to cover off. But I would want to truly understand what's made them say this. Reactivity can sometimes be helped with training but it tends more to be a lifelong 'condition' that you will always be managing and it does change life with the dog. Depending on where you live, it can severely change the walks you can do and when you can do them. Depending on friends and family, it can severely change when you can take the dog visiting and when you can't. And in my experience, it's not unusual for reactivity to also struggle to be left alone (i.e. they suffer from more than one anxiety-related behaviour) and this can make it all doubly difficult. Go into it with eyes open.