From what I can make out from a number of "Field Turf" web sites I looked at, it seems everyone is a bit right.
It looks like the turf can indeed be painted but it is only temporary. Painting can be used for advertising or when the field has different uses, such as switching from football to soccer etc., or special events.
For long term markings such as team logos and permanent field markings, they have to be specially made and sewn on as part of the field.
To be honest, none of the web sites was overly clear on the markings and I had to visit a number of sites to try and piece together what was intailed. Chance I might have interpreted the information incorrectly.
Guessing the installment of "Leaping Tigers" would involve a large financial outlay and permission from the City as well.