I can understand how it is slightly misleading to depict a photo of an EMR train that displays Luton Airport on its departure board. However, this style of advertising is very common these days.
For example, inside the terminal there are similar Thameslink adverts, with the tagline that "London is only a Thameslink away". This was very misleading as London at the time - the same as today - was not only a Thameslnk away, but a bus too. Does the DART now make this advert less bad? The jury is out on that one
There were also airport parking adverts with photo of a car next to a plane wheel with the caption "you can't park closer"
In conclusion, some small print never goes amiss for those who need absolute clarity on the product being advertised. On a serious note, for foreign people it is not obvious how to reach the city centre when landing in a new country for the first time. You could argue people should look this up ahead of time, but many people don't research very deeply, making do with a quick search of whether there is a train or not.