Nah, sorry, that article, or rather the show that the article is referring to, is almost certainly fake. I know about people being addicted to nasal sprays (me being one of them, unfortunately), and even addicted to the smell and/or taste of things, but those pictures are certainly fake. I won't suggest trying it out, so just believe me when I tell you that if you put Vapo rub on your eyelids, you will have red, watering eyes, you will end up with an infection quickly, and most importantly, the skin around your eyes will be red and sore. As you said, they tell you not to use it around babies because it's too strong - the skin on your eyelids is one of the most sensitive areas on your body, so it will have about the same effect. Not to mention being temporarily blinded by tears - which is very obviously not the case on the pictures in the article.
Also, eating it or putting it into her tea - try to do a steam bath with it. Two tablespoons in a bowl of water. It is so strong that I personally can't stand it. Makes me cough, my eyes water, my nose starts running like Usain Bolt on acid - now imagine having that in a tiny cup of tea. Or pure. Nah.......the entire show is pretty much a fix, and I am certainly not buying this one.
That said - having a phobia of throat and nasal sprays is not at all weird, and quite common actually. I have come across a lot of people who can't use those sprays. For a lot of people, having something squirted up their nose is a very unpleasant and sometimes even painful sensation, so they don't do it. It was a standard question when I used to work - 'Are you okay with using nasal/throat sprays, or would you like me to look for an alternative?' Just one of those things I guess. That's where the drops come in handy, or products like the tablets.