Urea>ammonia does trigger algae, and good. The severity of the proliferation will depends on the amount used.
Right now I'm running an experiment targeted at different responses of various plant species to differing nitrogen fertilizers. A - urea, B - ammonium, C - half ammonium, half nitrates, D - nitrates. All in the same amount [molar] and identical amount of other nutrients.
I can take some pics, if you insist, and let you guess which one is "algae infested" due urea or ammonium. You'll fail to pass, because all are pretty identical. Just a bit GDA.
I've tested this ammonium theory many times. Actually, I do test it permanently because, as a rule, I dose nitrogen by NH4NO3. Not that I never get troubles with algae, as well as any other possible mishaps, yet I've never, never, NEVER detected any sign of algae trouble in connection with ammonium dosing.
Now, why are our experiences that different? I don't know. I can say that unlike you, I never inject CO2, my lighting is on the moderate side, and my dosing is several times smaller than "average" EI. Yet to the latter I have to add that I've tested "true" EI as well, with half nitrates replaced with ammonium, and faced no trouble with algae, instead, signs of Mg & Ca deficiency due to way too high potassium.
That latter experiment is well documented and published here:
e-akvarium pp. 25-33.
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One more argument: Wherever you keep fish, ammonium is there. Inevitably. So, if your/Barr's theory holds, it is impossible to see a fish tank without algae problems.