There’s a signalling theory basis to this [1]. The BBB is a cheap signal, not a costly one, so it comes across as “trust me! I’m trustworthy! Look, I gave a bit of money to the trustworthy business people!” That is, it’s not a genuine signal of trustworthiness, so any effort expended on this signal may actually backfire: people might question why the business needs to send this signal in the first place.
On the topic of cheap signalling, a very long time ago, I was out to dinner with a friend. She was excited to try the place out, but as it turned out, the restaurant was pretty disappointing. "But it says 'Zagat rated' in the window!", she said.
I pointed out that they didn't have the actual score in the window & just because they rated it doesn't mean they rated it well...
There’s a signalling theory basis to this [1]. The BBB is a cheap signal, not a costly one, so it comes across as “trust me! I’m trustworthy! Look, I gave a bit of money to the trustworthy business people!” That is, it’s not a genuine signal of trustworthiness, so any effort expended on this signal may actually backfire: people might question why the business needs to send this signal in the first place.
[1] https://en.wikipedia.org/wiki/Signalling_(economics)