as far as I know the NS Records in the DNS doesn’t tell you anything about how a Organisation is handling it’s Mail-Traffic. For that you should check the MX Records in the DNS.  If you see there something with google.com they use google. Vice versa it doesn’t need to mean that the don’t use google if you don’t see it there, but it’s not so likely anymore.
On Windows that’s possible with “nslookup”, you just need to change the requested Record to MX.
On GNU/Linux it would be possible with host or dig. Host should give you the MX per default without any other parameters. With dig you need to “put -q MX” behind the program call. Like:
“dig -q MX big-fat-corp.com”
Does that makes sense?