Huh. I never heard anything like this about them. I started wearing underwires around 6 months in, and if it's restricted any growth, I haven't noticed it!
Personally, I think this might be a myth; if it were true, there'd be tons of medical professionals lining up to tell cis girls not to buy underwire bras during puberty, instead of the "teen department" having dozens of them. Maybe people got it mixed up with the fact that lactating mothers shouldn't wear *tight* bras, as it can restrict the flow of milk and that sometimes leads to mastitis...