Your Anthem may be different than my Anthem (in California, it is Anthem Blue Cross of California; Blue Shield is a completely separate company).
Last year Anthem stopped paying for trigger point injections with an E&M code. You could have the visit or the trigger points, but not both. Now at a visit we make the decision to do trigger points and schedule them for another day (we are pain management and the patient is coming in for monthly visit for medication review, among other things).
Anthem won't pay for an injection without a medication, even if that medication cost is zero. Lidocaine is usually bundled into the injection, but again, you have to go by what the payer has decided is right (as long as there is no fraud or other moral/ethical objection). We almost never do trigger points without depomedrol, or kenalog, or dexamethasone in addition to the lido (we use a 50/50 mixture of lidocaine and marcaine), so that's usually not an issue for us.
So I think the real issue is that you're billing an injection but not indicating the drug, which could lead them to think you're dry-needling, which is always considered experimental and therefore not covered. So you could bill the unlisted code J3490 if you want, or some say you could bill J2001 with a zero dollar amount (or one cent if your billing program won't let you do zero dollar charges).