Not completly True. Apart from particlar years when the banner delievered a major Blockbuster like 1995, 1998 or 2003, YRF and Dharma didn't dominated the Filmfare Awards. Let's see the data.
YRF was launched in 1973 and since then they have produced 90+ films (including their Y Films which produced films like Love ka the end and Mujhse Fraandship Karoge). which has won around 95 filmfares and 16 National Awards (i am not including films like Deewar and Trishul because they were not produced by YRF but directed by Yash Chopra). I am expecting a few more Awards this year for Siayyara so the count will increase to near 100 if the filmfare is not delayed further.
More than YRF i think it was the popularity of the YRF SRK pairing and the success of the family movies they made during 90s and early 2000s that contributed to most of their Awards. So before SRK YRF pairing, YRF made 14 films which earned 15 filmfares and 2 National awards. SRK and YRF worked in 10 films together which collectively won 40 filmfares and 6 National Awards (not including his cameo in Saathiya). This was the pairing which dominated the Awards with 10 filmfares for DDLJ, 7 for DTPH, 4 each for Mohabbaetin, Veer Zaara and JTHJ, 5 for CDI, 2 for RNBDJ and Darr and 1 each for Fan and Pathaan. Apart from this pairing the other YRF films which won major Awards were Lamhe (5 filmfares 1 National, Hum Tum (5 FF, 1 National), Saathiya (6 FF) etc.
Now lets look at Dharma. Dharma has done much better even without SRK even though in the beginning it was the Srk Dharma Pairing which made it a brand. Dharma Productions was started by Yash Johar but it struggled before Kuch Kuch Hota Hai. In the 50 years Dharma has produced 67 films which have won 80 Filmfares and 13 Nationals. Out of this, SRK Dharma pairing has yielded 25 Filmfares and 4 National awards in the 5 films they have worked in (Kuch Kuch Hota hai and Kal ho na Ho both won 8 filmfares and 2 National awards, K3G won 5 filmfares, MNIK 3, KANK 1). The other successful films of Dharma include Shershah (7 filmfares 1 National), Brahmastra (5 filmfares 4 National), Kill (6 filmfares), Rocky aur Rani (4 FF, 2 National) etc.
Apart from late 90s and early 2000s Yashraj and Dharma has not really dominated the Awards. Yes many of their Awards looks manipulated and that needs to be called out. But I guess nowadays every award ceremony is largely manipulated.