I don't believe this is true. If I have your SMS I am considerably more likely to be able to phish a recovery, even if recovery also involves something else. Every piece of information the attacker can get is valuable for forging auth.
What SMS is good at is being available. At this point cell phones are distributed to a massive portion of the world. But at this point smartphones can also act as U2F devices, I believe, so I'm not sure that benefit is so meaningful anymore.
Instead of companies wasting time on SMS 2FA they should be figuring out how to help their customers set up U2F.
I'd like to avoid being in a situation in 10 years where we have great options for end users available but 2FA SMS is still supported for legacy reasons, and unwitting users end up using it because it seems easier and they don't understand the risks.