Would it be a good idea to have bills transferred to my name to build credit?

i've never really heard of anyone doing this , my parents have this rental unit and its going to be coming vacant soon so they suggested they'd change the bills to my name ( hydro , gas ) so i could build my credit. and they'd pay them all

although i told them no rate away that i already had money issues and really didn't think it be a good idea as i would still be legally responsible for these bills if someone they were not able to pay them or whatever and i just didn't really want to deal with this. as its not my rental unit and don't want to get deeply involved with it

Updates
7 mo
haven't heard anything more about this from them and unit still isn't vacant , tenant is taking longer than expected to leave
Would it be a good idea to have bills transferred to my name to build credit?
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