Twilio outbounds the SMS message over the carrier network. Part of that relationship is that Twilio has to prevent spam from entering the carrier network, or the carriers will ban the interconnect.
Here's the full workflow of this situation.
The inbound leg looks like this.
[Spammer] -SMS-> [Carrier] -SMS-> [Twilio] -HTTP-> [Customer]
The outbound leg looks like this (the customer initiates this in response to the HTTP request)
[Customer] -HTTP/TWIML-> [Twilio] -SMS (SPAM DETECTION HERE)-> [Carrier] -SMS-> [Employee]
All of these parties are separate entities, each enforcing spam blocking. Twilio is incentivized to not transit spam over the Carrier because the Carrier will get upset at Twilio. Twilio has no way to tell the Carrier "Oh, hey, this is spam, but the customer owns the number and they said they were cool with getting spam, please don't get angry"