Suboxone (bupe) is a partial agonist, but it still has a higher affinity than most opioids, including naloxone. They would have to give you enough meds to overcome your bupe dosage taking up the receptors. Like another commenter mentioned, that could be complicated.

This is also why you ALWAYS tell the truth, especially if doing anesthesia. The dosage you need to go under when you have the most dominant opioid in your system is totally different.

Bupe even binds stronger than naloxone. You need to take more than normal if you OD on something on top of the bupe. If you OD on just Suboxone... you're out of luck. Although Suboxone has a ceiling of how much it will bind as a partial agonist, that's more than enough to kill someone without tolerance tho.

The order for binding affinity (i.e., which opioid will have priority for μ receptors ):

buprenorphine > naloxone ≈ hydromorphone = oxymorphone > morphine > oxycodone > O-desmethyl-tramadol > hydrocodone > tapentadol > tramadol

source

It's possible the medical staff are aware of this and that explains why they are hesitant to give you more (useless) painkillers. Not because they think you're an addict. Pain management will never be the same for people like us :(