Yes, you've got that right. Some chemicals facts that may be helpful to you and that are independent of product concentration or of pool size are the following.

For every 10 ppm Free Chlorine (FC) added by Trichlor, it also increases Cyanuric Acid (CYA) by 6 ppm.
For every 10 ppm FC added by Dichlor, it also increases CYA by 9 ppm.
For every 10 ppm FC added by Cal-Hypo, it also increases Calcium Hardness (CH) by at least 7 ppm.

So if you use stabilized chlorine (Trichlor or Dichlor), then the CYA will build up unless you have water dilution and you will need to keep raising your FC target higher and higher in order to maintain the same disinfection/oxidation level. If you don't, then the FC/CYA ratio can get low enough to allow algae to grow faster than chlorine can kill it which is why most algae reports in pools using stabilized chlorine tend to come in towards the latter part of the swim season when CYA levels have built up but where people have not raised their FC targets. One can avoid this problem by using unstabilized chlorine such as chlorinating liquid or bleach.

Thanks Richard. I've seen those numbers around the forum - and maybe in pool school too?

This is so key though for a TFP - you can't keep using CYA stabilized CL sources as that will drive you to an equilibrium point that is no longer sanitary. This is why I joined this site - it all clicked, made sense, had scientific basis.

I think some people get lucky with dichlor and trichlor because they have a good bit of splash and therefore water replacement. It would seem my father-in-law's pool is such an example: It used to get lots of use but with his youngest kids now using it less he has been fighting algae blooms more often.

Unfortunately, it's not a definite "if CYA gets high and the FC/CYA ratio gets low, you will get algae". Algae requires other factors other than a low or no active chlorine level in order to grow. It requires, first and foremost, to be there in the first place (not difficult given how many algae spores get blown around in air). Algae are photosynthetic like plants and require water (a source of hydrogen), sunlight, a source of carbon and oxygen (carbon dioxide or carbonates), a source of nitrogen (nitrates), a source of phosphate (orthophosphate), and other less essential nutrients as well as temperature to support reasonably fast growth. So some pool water may be low in nitrates, orthophosphate, or both and therefore limit algae growth even if the active chlorine level gets low.

Also, many people shock their pools weekly and that can somewhat make up for a low active chlorine level during the week. Some people use algaecides and in some cases even the chlorine they use contains an algaecide (some Trichlor pucks contain copper). And as you point out, water dilution can help keep CYA in check and is why smaller pools with backwashed sand filters and rain with overflow or lots of splashing tend to have lower CYA levels and not get algae. Finally, in some pools the CYA goes away over the winter so each season starts fresh. This may be due to bacterial conversion of CYA into ammonia and/or nitrogen gas and unfortunately when it goes to ammonia instead of nitrogen gas one can open up the pool to a huge chlorine demand.