There seems to be some confusion here. In India, an "entry visa" is a specific category, distinct from a tourist visa, student visa or business visa. It allows entry to people who are not tourists, students, or on business, etc.

That said, I think the OP is over-thinking this. The invitation letter can be submitted as part of the application, to justify the visit, but it is not an official document. The consulate isn't going to say "The invitation says entry visa, but you're not eligible vide rule 39552(c) Sec 1123, so off with your head". They will give her the appropriate visa, which could be an entry visa---the rules seem ambiguous. So the letter is fine, but one should talk to the visa issuing office before applying for a specific type of visa.