When scientists say there is "no evidence" they mean there hasn't yet been a long-term study on this specific vaccine - but that doesn't mean there are no facts here at all or we're shooting in the dark.
In fact, Prof Chappell pointed out, there is lots of evidence from other non-live virus vaccines, including the flu jab, that they have no impact on fertility and are completely safe and recommended for use during pregnancy.
And getting the Covid virus itself - which the vaccine protects against - could affect fertility, so "you're much more likely to have fertility issues post-Covid than after the vaccine," Prof Stonehouse said.
False placenta claims
Some of the rumours have suggested the vaccine could threaten fertility because it contains proteins also used to make the placenta. Posts on social media have claimed this could lead the body to attack the placenta.
This is not true - the vaccine does contain a protein which slightly resembles one used in the development of the placenta but it's not similar enough to confuse the body.
Vaccines are designed around the most distinctive parts of the virus's spike to make sure it recognises only that.
The fact that the respective proteins bear a passing resemblance "doesn't mean anything", says Prof Chappell, since there are lots of similar proteins existing in different places in nature - it's their precise length and sequence that makes them distinctive.
Prof Chappell, who specialises in the health of pregnant women and people hoping to conceive, said she had "no concerns" about fertility and the Covid vaccine.
And the deputy chief medical officer for England, Jonathan Van-Tam, when answering questions from BBC viewers, said: "I have never heard of a vaccine that affects fertility."