I've extensively researched, and trust, the purity level of the high quality, therapeutic level essential oils I have used for the last 2.5 years (I can direct you to a source privately). There are likely several essential oil companies that buy SOME of their essential oils from tested, safe sources also. I don't know much about other companies, so I can only speak for the one I know well. It can be very enlightening to compare various essential oils. Please DO check the ingredient list of any company's essential oils? They sure don't have to say if they're diluted with water.... but they should list if they're diluted by carrier oils (like jojoba or almond oil), and/or have other additives.
And please do skin test any essential oil for sensitivities you may have, before ever trying it internally? I do this by rubbing one drop on the skin inside of my elbow. Have a carrier oil handy if it's too "hot", or starts to cause a rash. Carrier oil will dilute it. Water will not! Check your elbow again in 3 hours. No reaction? Then you should be able to use it on the neck, stomach, feet, etc... wherever you need it most... without dilution. If it was too hot, use it diluted. If you show a sensitivity, please try a different essential oil that can address what you need. That's one of the huge perks of essential oils... their chemical complexity lends to multiple "side benefits" :-).
Many essential oils should be diluted for children, elderly, and those that are sensitive. A rough guide to a 3% diluted solution is 3 drops of essential oil to 1 tsp of carrier oil. For an approximate 1% solution, use just 1 drop of essential oil in 1 tsp of carrier oil. Mixes can be done in a shot glass... stirred... and then use the amount you wish to, and store in your medicine cabinet. Leftovers should keep for a day or two.