Really..? People do say that? That's a gross oversimplification of the problem of learning a language.
Learning Cyrillic is nothing compared to learning pronouncing, listening, grammar and vocabulary.
There are hundreds of words and grammar and conjugation rules to learn but 33 (or less, due to sharing) letters (and similar style ones, not Arabic ones or Chinese characters or Hangul ones) are a major obstacle?
Differences and amount of letters between Cyrillic and Latin is also nothing compared to how out there Chinese, Arabic, Thai, etc. systems are. It's so simple and similar and there's so little of it that it's as much of not an obstacle as it can be without being the same script.
Learning a language is always hard and learning most languages you'd have to learn a new sound for every Latin letter (and for many of its di and trigraphs used in the new language) as well anyway because it might be pronounced differently and you'd better not "cheat" by going letter -> English sound -> new language sound in your head because that's an obstacle and artificially slowing yourself down or possibly making a mistake.
Even though a lot of vocabulary, grammar and the script are shared between English, French, Dutch, Spanish, etc. it's not such a foregone conclusion that people can just do it effortlessly (with less effort than Chinese but it's still quite an effort).
Similarly I read accounts of Westerners taking Japanese Language Proficiency Test and mentioning a lot of Koreans and Chinese being there due to probably having less obstacles with Japanese (Korean supposedly has similar grammar and Chinese of course has similar writing system) but of course CJK languages are not mutually intelligible and a Korean, Japanese or Chinese person can't just up and go pass a language test in one of the other two easily.
Polish uses Latin and some diacritics but it's not any easier for it (it might actually be harder due to the language itself).
Ashens (a YouTuber who eats weird stuff) once pronounced wafelek jagodowy as it were English and it was so butchered he might as well have recited a Cthulu summoning instead (you can compare the two on Google Translate). I'm not jabbing at people who don't know Polish but I'm trying to illustrate that it just doesn't work that way - a Polish j or w is not an English j or w.
Cyrillic also doesn't pervade Poland at all and I don't know Russian but I had it at school so I know Cyrillic and having native Polish I can sort of get some Russian but an American who knew just Cyrillic would just get nothing. I also get nothing out of Kazakh in either script, Turkish, etc. but looking at any Slavic language or French I can get a lot of words due to similarities to what I do know.
On the way to fluency (whatever definition of it you might consider) you'll run into sounding natural in both sound and vocabulary way more often than anything else. E.g. former ambassador to Poland was considered by everyone to have great Polish (for an American that is..) and often spoke Polish when invited on TV and such and understood spoken and written Polish seemingly perfectly but you could tell as soon as he opened his mouth he's absolutely not a native speaker due to his pronunciation (and it's not just an accent, people from Podlasie have an accent when they come to Pomorze and vice versa, with him you could just tell he has an un-Polish vocal system producing Polish sounds) and he received ambassador language training USA does and has been living in Poland for years.
And I'm saying all that as someone with some interest in linguistic, writing systems, etc. for a while now and knowing 3-to-5-ish writing systems (Polish/English/Latin, Russian/Cyrillic, Japanese katakana and hiragana and few dozen kanji I can write and few hundred I can read - it's technically one "writing" system but it's more like a 3-in-1 because they represent same sounds but in different contexts and with different meaning or lack of it - it's a complex deal) and 2 languages really well (English, Polish) and 2 other badly (failed Russian, absolute beginner Japanese). I know this doesn't make me an expert but at least I've been around the languages a bit more than an average person.
I actually wish my biggest obstacle with Japanese was just learning all of katakana and hiragana (which there are almost 50 of each, plus diacritics and digraphs with them, and they are much different from Cyrillic and Latin) because I've done that long ago with very little overall effort using just Memrise and Obenkyo on my phone whenever I could spare a moment over a few weeks.