A former bodyguard for Brian Thompson, the UnitedHealthcare CEO who was shot and killed in NYC, is in complete disbelief the exec didn't have security when he was murdered.

Philip Klein, whose Texas-based security firm Klein Investigations previously provided bodyguards for Thompson in the 2000s, tells TMZ ... he is "shocked and baffled" to see the high-profile CEO didn't have a "detail" (at least 10 security guards) with him while out and about in Manhattan -- given the malevolence the insurance industry often faces.

He also says Thompson should've been wearing a vest in addition to having guards by his side, but adds ... he likely didn't have it on due to personal preference.

Philip believes it's now UHC that has some explaining to do regarding Thompson strolling solo into the Hilton, as the late businessman should have never been out by himself. But, again, it is ultimately his choice.

He says Thompson was a "nice guy, who was a real go-getter" when he was covering him ... yet, he isn't surprised the CEO might have had a target on his back.

As Klein puts it ... it is common knowledge the insurance biz generates a lot of hostility, noting Thompson's death should be a "lesson" to other major corporations -- their CEOs and executives need to be protected.

As TMZ previously reported, Thompson was fatally shot outside of the New York Hilton hotel Wednesday morning. Police have described it as a "premeditated, preplanned targeted attack" ... because the assassin was seen lurking around the scene minutes before Thompson arrived.