They usually do, but these only protect from grid failures. HEX certainly does have battery + generators (it's one of the most important DC's in the country).

Components inside the DC should be redundant, but the customer can decide whether to have dual power feeds from redundant areas of the DC provided to their rack/cage.

Even with all this, issues do happen, Telecity had a very high profile and prolonged issue at the end of last year that affected AWS & Azure amongst others: http://www.theregister.co.uk/2015/11/18/telecity_outage_fix_...