Regarding a story in Shiva Purana
Yes. In that kalpa when this incident happened, Lord Brahma emerged from lord Vishnu but was under the maya(illusion) of Lord Shiva and hence he argued with lord Vishnu over superiority.
20-21. At the sight of that beautiful form I was struck with wonder. On seeing the four-armed Nārāyaṇa, shining like Kāla, of golden hue, the immanent soul of all in that form, of large arms depicting the Sat and Asat in Himself I became delighted.
- Deluded by the illusion of Śiva, the sportive lord, I could not recognise my progenitor in him. I addressed him with delight.
There is one interesting thing to notice here. Lord Vishnu says this to Lord Brahma when he argues with him.
Viṣṇu said:— “I know you as the creator of the world. For the sake of creation and support you are descended from my undecaying limbs. You have forgotten me, who am a lord of universe, abiding in waters the salubrious, the supreme soul, invoked by many, praised by many, All-pervasive, imperishable, ruler, the source and origin of universe, the longarmed and the ommipresent lord. There is no doubt in this that you are born of the lotus from my umbilicus.
36. “Of course, it is not your fault. I have exercised my power of illusion over you. O four-faced one, listen to the truth. I am the lord of all Gods.
Now here, one may argue that Lord Brahma was also under the maya of lord Hari. But this is not the case, we also need to notice the last line of the sentence which Lord Vishnu spoke.
I am the lord of all Gods.
Now, this line makes it clear that he was also under the influence of Maya of someone. We come to see in the later part that the whole time this incident was going on, lord Vishnu was also under the maya of Lord Shiva.
When lord Brahma and Vishnu were not able to figure out the end of the linga, they bowed to Lord Maheshwara.
62.From a desire to know its top as quickly as possible I exerted myself and was exhausted. Unable to see the top I came down after some time.
Similarly, lord Viṣṇu, the lotus-eyed, too became weary. Appearing like the lord of everything in his huge body he too rose up.
As soon as he came up, we bowed to Śiva again and again. He stood aside with a gloomy mind as he too was deluded by the illusion of Śiva.
We bowed down to Liṅga at His back, sides and in front. He mused within himself “What can this be?”
Also, this line makes it clear ever further.
Thus performing obeisance and prayer to quell our earlier pride, O foremost of sages, we spent a hundred autumns therein.
So, in a nutshell, the answer to your question is as follows:
Lord Brahma was under the illusion of Lord Shiva and hence argued with Lord Vishnu.
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