He knew, if you are a second time buyer, the odds were very high that you could go to at least 437.5k if you/wife wanted it enough (87.5k would be 20% deposit unless you got an exemption).That's just estate agents and vendors. They would do that even if they didnt know what your maximum amount was. I bought the house I'm in 3 years ago. We had sold and moved into my parents for a few months. House went up for sale. Wife viewed it on the first weekend and loved it. Asking was 380k. I went straight in at 400k and my offer was valid for 24 hours only. Needless to say there was an offer shortly after for 405k and in the end we were old the vendor wanted to 420k and the first to bid it got it. I only had approval to 350k, the rest was cash so he had no idea what i was playing with but it still went there.
No guarantees this made any difference (or that you're a second time buyer) but maybe it made the difference between you being told the vendor wanted 420 vs 410. So why let someone on the other side of the table know? Especially when they have a lot more experience at selling houses than you have buying them.