How does sending compressed points in ECC can limit the attacker's capabilities?
If the implementation is using uncompressed point exchange, The attacker gets an opportunity to supply points to Bob that are not in the Curve which was selected by Alice and Bob. The attacker will supply points to Bob that are in curves of a lower order which makes it possible to estimate Bobs secret.
Therefore if the implementation ensures that Bob has to calculate the point then he will come to know that the point being provided is not on the curve selected by Alice and Bob in the first place and will result in coming to know about the attack or the corruption.
Two basic constructs in ECC are the standard curves and Implementation by programmers. The argument is should use of compression be specified in the standard or should be left to the implementation. Since compression is so important for ensuring security it should be made part of the standard( As per the presenters ) to prevent implementation errors.