To me, those are very different.
An infant doesn’t care on unless they need something and aren’t getting it. There’s no reason for an infant to get to the pint of hysterical before the caregiver tries SOMETHING. Now, the infant may build to hysteria even if the caregiver (parent, nanny or other) is trying to find the issue.
On the other hand, toddlers and preschoolers can start to learn to differentiate between small, big and in between. I offer an ice pack for bumps, not stubbed toes, just like I offer bandaids for bleeding but not scratches. By assuring a young child that it’s a small pain, but it’ll be over soon, I acknowledge that it hurts and assure them that it won’t last. A kiss on the forehead and “I know your toe hurts, but it’ll be okay soon. Do you want to get out the kid dishes or silverware first?” redirects their attention to something else. However, repeating the same phrase over and over, never redirecting attention is counter-productive, as the child focuses on what you are saying.
However, I work with families who have the same views. To me (and my families), being loving doesn’t mean large reactions to small situations. If you prefer a different view of loving attention, interview again. Ask open-ended questions about situations which would bother you (baby starts crying while on a walk with nanny and nanny needs to get home quickly, older child has various levels of pain, etc). Don’t give your views, listen to see what the applicants say.