Gov. Mike Pence (R) seemed very frustrated Sunday as he struck back at critics of Indiana’s Religious Freedom Restoration Act (RFRA), claiming that they spread disinformation about the law he signed last week.

“This is not about discrimination,” Pence insisted. “We’ve been doing our level best to correct the gross mischaracterization of this law that has been spread all over the country.”

But Pence didn’t correct the record. He obfuscated, dismissing legitimate concerns and attacking those who harbor them. RFRA’s potential discriminatory effects are somewhat indirect, but make no mistake: Indiana’s new law could facilitate discrimination against gays and lesbians across the state.

RFRA instructs courts to treat government actions that infringe on people’s religious practices with the highest legal scrutiny. Few government actions can survive that sort of review — including, perhaps, the application of municipal laws barring discrimination against gays and lesbians. That’s why RFRA supporters claim the law ensures that, say, devout Christian florists won’t have to provide their services in a same-sex wedding. If a local anti-discrimination ordinance required those florists to service a ceremony to which they objected on religious grounds, they could challenge the application of that ordinance in court, and the legal balancing that RFRA demands would tip the scales more in their direction.

Pence appeared to base his defense on the fact that the law didn’t immediately wipe away local anti-discrimination ordinances in Indiana; but RFRA is nevertheless a direct threat to the full application of local anti-discrimination laws if and when challenged in court. Pence then seemed to argue that Indiana doesn’t need laws banning discrimination against gays and lesbians, because Hoosiers are nice people who don’t discriminate; perhaps he should tell his supporters, those brave defenders of reluctant florists. Pence also argued that a score of other states and the federal government have RFRA laws of their own, pointing out that Bill Clinton signed the federal version two decades ago. That doesn’t help his case — RFRA laws had serious potential downsides back then, too.

It’s true that RFRA has implications well beyond issues of LGBT rights, affecting the treatment of all sorts of religious claims in court; it should also be judged as a policy that could, say, help the Amish, Native American tribes or other religious minorities minimize the impact of majoritarian laws on their traditional ways of life. If Pence and RFRA supporters think that religious believers in the United States require more legal deference and protection, and that it’s worth the risk of entrenching legal discrimination and accepting various other tradeoffs to achieve it, they should make that argument. But they can’t credibly claim that it’s outrageous to worry that Indiana’s RFRA will promote discrimination.