Yes. If the EU accepted the Chequers deal this would leave the UK with more power than the remaining members of the EU. A good summary is the BBC article on the subject but I'll quote the document directly for the remaining of this answer (emphasis is mine).
1) The UK agrees to use the common rulebook but wants the same power as before brexit in negotiating the standards. Also the UK wants to retain the possibility of refusing to follow those same standards. It mentions that it understands that this would have consequences but, at this point in the document (see the next point) presents no legal framework to deal with it effectively leaving the consequences in legal limbo. Finally it puts "services" out of the deal.
I. POSITION ON THE FUTURE RELATIONSHIP
a. The UK and the EU would maintain a common rulebook for all goods including agri-food, with the UK making an upfront choice to commit by treaty to ongoing harmonisation with EU rules on goods, covering only those necessary to provide
for frictionless trade at the border.
The UK would of course continue to play a strong role in shaping the international standards that underpin
them, and Parliament would have oversight of the incorporation of
these rules into the UK’s legal order –
with the ability to choose not to do so, recognising that this would have consequences.
We would strike different arrangements for services, where it is in our interests to have regulatory
flexibility, recognising the UK and the EU will not have
current levels of access to each other’s markets
2) It mentions that the regulation would be jointly done with UK and EU courts but only considering the rules the UK agreed to follow of the rulebook.
The UK and the EU would establish a joint institutional > framework to provide for the consistent interpretation and application of UK-EU agreements by both parties. This would be done in
the UK by UK courts, and in the EU by EU courts –
with due regard paid to EU case law in areas where the UK continued to apply a common rulebook.
3) The UK wants to collect EU and UK tariffs in order to be able to maintain different rules depending on the partner country (organization).
d. The UK and the EU would work together on the phased
introduction of a new Facilitated Customs Arrangement
that would remove the need for customs checks and controls between
the UK and the EU as if a combined customs territory. The UK would apply the UK’s tariffs and trade policy for goods intended for the UK, and the EU’s tariffs and trade policy for goods intended for the EU - becoming operational in stages as both sides complete the
necessary preparations. This would enable the UK to control its own tariffs for trade with the rest of the world and ensure businesses paid the right or no tariff - in the vast majority of cases upfront, and otherwise through a repayment mechanism.
4) No longer follow common Agriculture and Fisheries policy:
d. mean that the UK will leave the Common Agricultural
Policy and Common Fisheries Policy – taking back control of UK waters as an independent coastal state and designing a domestic agricultural policy that works in the best interests of the UK;
5) No longer accept the jurisdiction of the CJEU (Court of Justice of the European Union):
restore the supremacy of UK courts, ending the jurisdiction of the CJEU in the UK, with no more preliminary references from UK courts, but committing that UK courts would pay due regard
to the CJEU’s jurisprudence where the UK had chosen to apply a common rulebook to ensure consistent interpretation;
6) The UK wants to leave the free mobility of EU citizens out of the deal:
end free movement, giving the UK back control over how many people enter the country;
7) Ending the financial contributions to the EU:
end vast annual payments to the EU budget, with appropriate contributions for joint action in specific areas, such as science and innovation, releasing funds for domestic priorities – in particular our long-term plan for the NHS;
Michel Barnier dismissed the proposal almost immediately. Many of the points of the agreement would leave the UK with far more power than a normal EU member which pay contributions, follows EU court jurisdiction, follows the freedom of movement principle, and cannot cherry pick which sectors to apply the rules.
The document is also fairly populist often making unnecessary remarks (that almost look like campaign banners) where none was needed. It clearly seems like a document for internal consumption and trying to appease the more nationalist factions of the Tory party.
- mean that the UK will leave the Common Agricultural Policy and Common Fisheries Policy – taking back control of
UK waters as an independent coastal state and designing a
agricultural policy that works in the best interests of the UK;
- end free movement, giving the UK back control over how many people enter the country;
- restore the supremacy of UK courts, ending the jurisdiction of the CJEU in the UK
- end vast annual payments to the EU budget, with appropriate contributions for joint action in
specific areas, such as science and innovation, releasing
funds for domestic priorities