"The rule "to check an unstressed vowel by altering a word" assumes the person is fluent in spoken language. It is the way Russian school-children learn spelling in the elementary school classes. They speak Russian intuitively and they do not make mistakes in declension, conjugation, pronunciation and stress positioning. For example, let's consider the noun "головА" "head" (I capitalized the vowel which is stressed). Due to the vowel reduction, it is normally pronounced as [ga-la-VA] (I intentionally ignore phonetic nuances like schwas etc.). A Russian child of 7 - 8 y.o. may be unsure what is the right way to spell this word: галава, голава, галова or голова. Children of that age often do similar spelling errors of this sort.
At school, children are taught to аpply the "checking" rule. To check the first unstressed vowel, one can use Singular Accusative (which is "гОлову" [GO-la-vu]) or Plural Nominative ("гОловы" [GO-la-vy], "heads"). In the both examples, the first "о" is clearly heard. To check the second unstressed vowel, one can use Plural Genitive ("голОв" [ga-LOF]) or the diminutive derivаtion "голОвка" [ga-LOF-ka], "little head". The second "о" is clearly heard now. Thus, the only correct way to spell the original word is "голова", although the first two vowels аre phonetically "unclear".
However, when teaching Russian spelling to nаtive children, it is assumed they have no doubt in how to derive all those forms and where to put stress in them. They do it intuitively. As I stated it above, this can hardly be used by non-native adults who only started to learn Russian.
Foreigners need a different approach, quite the opposite! First, they just have to memorize the "dictionary form", both its spelling and its pronunciation. They have to remember it is "головА" with two unstressed о's and the stress on the third syllable. Then, they learn cases and endings. One of the difficulties they are facing to is that the stress is sometimes shifted in different case forms, although there are some regular patterns for it. So, they learn that Accusative of feminine nouns (ending in -а) is formed by replacing "-а" with "-у". In some nouns, the stress is shifted from the final syllable to the first syllаble when getting Accusative, and "головА" is one of such nouns.
If a foreigner does not remember the spelling, they cаn be confused how the Accusative needs to be pronounced: is it [GA-la-vu] or [GO-la-vu]? That is why the spelling needs to be memorized first. Then the foreigner will know the first vowel is "о", and so they can get the correct Accusative form which is pronounced as [GO-la-vu].
However, the Russian spelling is still pretty simple if compared to English or French spelling. The two basic issues with the Russian spelling (where native children do errors most frequently) are 1) unstressed vowels (А/О and И/Е/Я) and 2) word-final consonants (which are devoiced, so one has to decide between П-Б, Т-Д, К-Г etc. when writing).
If you compаre this with the English spelling, the English spelling will seem a "true nightmare" for you! Meet-meat-mete, night-knight, rite-right-write, weather-whether-wether and so on, and so on... So, it is just wrong to think Russian spelling is hard. " (ц.)