I don't think this is awkward at all. The man pushing the wheelchair is (I assume) her employee.
I would no more expect Liz's fiance to take over her nurse/caregiver's duties than I would expect him to start doing her laundry, scheduling her appointments, cleaning the pool, or performing any other chores for which she has paid staff simply because they are engaged.
I think the reason we so often see spouses or loved ones pushing wheelchairs or performing other caregiving is because private attendants are priced out of reach for most of us. Ms. Taylor is fortunate enough not to have cast her sweetheart in the role of nurse.
I couldn't agree with all this more.
I have no real idea what it would be like to be in a wheelchair - but I think that, if I could afford it, as Liz Taylor clearly can, I would very much like to have the aspects of my physical condition that are limiting be handled/enhanced by paid employees, so that I could 'walk' alongside my fiancee as much as I could. I would want to mirror, as closely as physical possible, what it would be like WITHOUT my limiting physical condition.
And I completely agree that most people simply don't have that luxury. Ah, to be a rich as Elizabeth Taylor! ::sighs wistfully::