"A group that X" or "A group who X"? (American English)

I’ve been asked to proofread a company newsletter, and I came across this line:

[Department name] is something special – an elite unit who finds
opportunities where others cannot.

Should it rather be "an elite group that finds opportunities where others cannot"?

It seems to me that the relative pronoun for a "unit" would be "that" rather than "who" even if the unit/department is made up of people. Am I correct?