The tooling people are wrong, sounds like the guy doesn't have much experience with cutting tools and metals.
300 series stainless is not a hard metal, it is a tough metal. The difference is that a hard metal can not easily be deformed by with a hammer, a tough metal can. Tough materials molecules don't separate easily they tend to cling and gall which makes them "tough" to cut, these different qualities makes tooling knowledge and selection critical.
You have to cut hard materials with hard cutting tools but when making holes in tough materials you must use a tough cutter not a hard cutter or you will get what you got broken tools. Instead of carbide drills and reamers get some M42 cobalt drills and reamers, they are tough much tougher and will resist shock and breakage and they are not as hard and brittle as carbide. Slow down to approximately 60 sfpm, .004 IPT chip load.
For a 3/8" drill, run a peck drilling cycle (G83/G73) at about 750 RPM and 3" per minute feed, run the reamer using a reaming cycle (G85) at about 8" per minute. The other benefit of tough tooling is that cobalt tools are a lot cheaper than carbide.
Maybe thats why the guy recommends carbide tools...