This curl command works as desired:
curl -H \"X-Api-Key:j65k423lj4k2l3fds\" `
-X PUT `
-d \"alerts_enabled=true\" `
https://some/working/fi
got it to work natively using invoke-webrequest. powershell guru here at work helped me out. Switched to the New Relic API version 2 (available at https://rpm.newrelic.com/api/explore), which uses JSON instead of xml, and made some sytax tweaks.
$json = @"{"alert_policy":[{"enabled":"true"}]"@
$headers = @{}
$headers["X-Api-Key"] = "j65k423lj4k2l3fds"
Invoke-WebRequest -Uri "https://some/working/file.json" -Body $json -ContentType "application/json" -Headers $headers -Method Post