I'd expect any company to get my consent before requesting references from current or past employers. First of all because I can direct them to relevant people but most importantly because it's not public information. I had cases in the past where I asked them to hold off with checks until I have signed a contract and quit the other job (under the condition that the contract would be void if the check fails). That way they could confirm that my story was correct without telling my employer that I plan to quit.