Well they are wrong.
EM fields generated by substation transformers are 50Hz frequency. Mobile phones and wi fi operate at much higher frequencies in the GHz range.
The EM fields behave differently, in the respect that shielding a 50Hz field is very difficult, but shielding a GHz field is very easy. That is why for 5G phones there are going to be a lot more aerials, because it is easier for the high frequencies to be blocked. As a homeowner, it is conceivable that you could eliminate all GHz frequencies within your home with shielding (think thin aluminum plates on all the walls, plus film over the windows, and filtering any inlet lines. You could essentially turn your house into a Faraday cage for GHz frequencies at relatively low cost, like that guy who lived in a truck in Enemy of the State. It's not conceivable to shield your house from substation EM fields because there is no practical material thick enough.
Generally transformers are designer to keep all the em fields inside because that makes them more efficient. There is no benefit to spraying EM out into the space around them. Modern ones are probably much better at this than older ones.
How dangerous high frequency EM fields are compared to low frequency EM fields I have no clue. You should bear in mind though that the electrical wiring in your house emits 50Hz EM fields, and if the sub station is far away, it may be that you get far greater fields from the wiring in your house than actually from the substation.
If you were really concerned about it, you could probably pay for a survey from someone who could survey the house and check whether the EM fields fall within or outside any guidelines. I am not sure whether there are guidelines for domestic premises, but I think there probably are for industry. You can search on the web.