You seem to be one of those who have approved the edit (unfortunately, the post has been vandalized by another user since then), so I guess (correct me if I'm wrong) this question's goal is primarily to confirm your original thought.
"Is it offensive?" question seems to be subjective because it can't be measured. I would say yes, someone else would say no, and we end up in a "word against word" battle. So let me focus of facts only.
Official name of Kyiv. According to UNGEGN (United Nations Group of Experts on Geographical Names), the only possible English-language transliteration is "Kyiv".
The same source confirms the proper spelling for Donets'k, Luhans'k, Kharkiv, and several others.
Kyiv in other languages. Besides "Kiev", there are other spellings, including "Kiew", "Kijów", "Kænugarður" and even 《基辅》, pronounced — believe it or not —
[ji-fu]. When visiting countries where this name is accepted, everyone would understand you, despite the fact these names are not internationally-accepted.
People's perception. Indeed, spelling "Kiev" is a direct transliteration of "Киев", the Russian word for Kyiv, and many Ukrainians (not all, however) associate this with the Russian occupation that happened in the past and the armed invasion and partial occupation that occurs at the moment.
The following photo shows the very process of russification. "Little green men" in unmarked uniforms on a military truck "enforce" the Russian spelling of a road sign at the entry to the occupied Donets'k city by removing the "soft sign" so that «ДОНЕЦЬК» became «ДОНЕЦК».
Most obviously, this produces resistance against the "Russian-based" spelling of toponyms among the Ukrainians. Like myself.
Many Russian officials also insist on using an incorrect spelling "the Ukraine", too.
This, multiplied to the fact that many Ukrainians speak bad English, don't simply care, or actively refuse to recognize Ukraine as a country, has a certain effect, as shown in JonathanReez♦'s answer.
More to go. Having several names for toponyms (for various historic reasons) happens in other countries, too: Burma/Myanmar, Cambodia/Kampuchea, Mumbai/Bombay, Munich/München/Monaco, Beijing/Peking, Saigon/Ho Chi Minh City, Bangkok/Krungthep Mahanakhon, Falkland/Malvin Islands, to name a few.
A Traveler's Rule of Thumb (mind you, we are at Travel.SE). A traveler should always consider the historical and cultural aspects in order to avoid being perceived as an ignorant person (or, in boundary cases, as an enemy's agent).
However, there is no problem if a foreigner uses Russian as their way of communication. Check this question for further details: What is the main spoken language in Kiev: Ukrainian or Russian?
Also, related: Does anyone want Ukraine to be called “the Ukraine”?