Gag orders aside, is there any evidence that a national security letter can be used to compel a company to create or help create a backdoor like that?

Everything I've seen about NSLs says that they allow the government to compel production of (some) information about an individual or group if they say it's part of a national security investigation. As I understand it, the big objection to NSLs from groups like the EFF and ACLU is that they're outside the normal system of court order and subpoenas, lack enough restrictions on when they can be used and have the gag order provision...not that they give the government power to ask companies to do whatever they want.