401 Unauthorized when trying to access JIRA OnDemand REST API

Cross-post AOD-7395, I am sorry about that I would have filed this as query rather than bug but that is not an available option.

Recently trying to access JIRA OnDemand REST API using basic authentication results in error code 401 - unauthorized. Tried anything possible (curl) as documented for example here https://developer.atlassian.com/display/JIRADEV/JIRA+REST+API+Example+-+Query+issues

Even simple call to /rest/api/2/serverInfo fails.

However when logged in using browser, call to the same URL returns correct JSON:

{ "baseUrl": "https://base.url.com", "version": "6.4-OD-04-006", "versionNumbers": [ 6, 4, 0 ], "buildNumber": 64001, "buildDate": "2014-08-20T00:00:00.000-0500", "serverTime": "2014-08-27T00:55:05.782-0500", "scmInfo": "b1633a7e36a916f95ac968aafe0f8b849ce804e3", "serverTitle": "JIRA" }

Are there any changes in authorization? Does something need to be setup on server side?