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
11 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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