same problem for me, i wrote letter to Motorola,emailed them phone call, service centers, but everything failed, last wish of me is to go to consumer court.
Letter i wrote: HELLO MOTOROLA,
This is Manoj from Chennai, I would like to thank for the best Android phones you offer us,Let to come to the point, I have brought moto g 3rd gen via flipkart 2 weeks back, I brought the phones for my cousin (10 year old boy) , he mistakenly forget the email id or phone number they entered, they did factory reset after that, we unable to open the phone its locked, asking for email/password and phone but none of the above works , please help, we gone to Motorola customer service representative in t.nagar Chennai, but they also opened their hands and failed to help us,You’re the only trust I believe you Motorola, I can send you the imei numbers / flipkart buyer details too, help me to get out this security issues.

no use they opened their hands,

even custom rom cannot be installed in moto g3 without roorting and having access.

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http://www.gammerson.com/2015/08/downloa...d-gen.html

I TRIED MANY WAYS, AS EXPERT- I CANNOT FIND A SOLUTION, this problem exist only for 1 out of many many thousands,