That's not entirely accurate. Halo: Reach showed us how Spartan III's can do everything a Spartan II can but it also showed us how expendable they are.
But in terms of "humanizing the haloverse" that award goes to Halo 3: ODST which came out a year before and for the first time put us in the shoes of somebody who's not a Spartan.
I think Reach focused / showed us more of the harshness of the war. People dying everywhere from space to the city to the countrysides of Reach. Also we lose like 4 times in the campaign:
- sword base, while yes we shoo off that corvette, the base is later lost to the covies
- Space, we blow up the super carrier at the cost of Jorge's life but then 100's of other covie ships show up
- We evacuate civillains and try to beat back the covenant above New Alexandria but then the citiy is glassed and Kat dies
- Noble 6 saves the Autumn and by extension humanity, but he / we die alone, on a doomed world, surrounded by enemies (kind of like Caesar did now that I think about it)
So ODST added the humanity with the audio story and the ODST gameplay but Reach showed the harshness of the 30 year long war.